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(xxii) The positive square root of mean of the squared deviations of X_{i}(i=12 \ldots \ldots n) observations from their arithmetic mean is called(a) harmonic mean(b) range(c) standard deviation

### (xxii) The positive square root of mean of the squared deviations of X_{i}(i=12 \ldots \ldots n) observations from their arithmetic mean is called(a) harmonic mean(b) range(c) standard deviation

(xv) The most frequent occurring observation in a data set is called(a) mode(b) median(c) harmonic mean

### (xv) The most frequent occurring observation in a data set is called(a) mode(b) median(c) harmonic mean

1. What do you understand by measures of central tendency?

### 1. What do you understand by measures of central tendency?

Example 2: Find the Range for the following distribution.\begin{tabular}{|c|c|}\hline Classes / Groups & \boldsymbol{f} \\\hline 10-19 & 10 \\\hline 20-29 & 7 \\\hline 30-39 & 9 \\\hline 40-49 & 6 \\\hline 50-59 & 7 \\\hline 60-69 & 1 \\\hline Total & 40 \\\hline\end{tabular}

### Example 2: Find the Range for the following distribution.\begin{tabular}{|c|c|}\hline Classes / Groups & \boldsymbol{f} \\\hline 10-19 & 10 \\\hline 20-29 & 7 \\\hline 30-39 & 9 \\\hline 40-49 & 6 \\\hline 50-59 & 7 \\\hline 60-69 & 1 \\\hline Total & 40 \\\hline\end{tabular}

(vi) Arithmetic mean is a measure that determines a value of the variable under study by dividing the sum of all values of the variable by their(a) number(b) group(c) denominator

### (vi) Arithmetic mean is a measure that determines a value of the variable under study by dividing the sum of all values of the variable by their(a) number(b) group(c) denominator

Example 2: A variable X takes the following values 45862 . Find the mean of X . Also find the mean when (a) 5 is added to each observation (b) 10 is multiplied with each observation (c) Prove sum of the deviation from mean is zero.

### Example 2: A variable X takes the following values 45862 . Find the mean of X . Also find the mean when (a) 5 is added to each observation (b) 10 is multiplied with each observation (c) Prove sum of the deviation from mean is zero.

(iv) A cumulative frequency table is also called(a) frequency distribution(b) data(c) less than cumulative frequency distribution

### (iv) A cumulative frequency table is also called(a) frequency distribution(b) data(c) less than cumulative frequency distribution

Example 3: For the following data showing weights of toffee boxes in gm. Determine the modal weight of boxes.\begin{tabular}{|c|c|}\hline Classes / Groups & Frequency \\\hline 0-9 & 2 \\\hline 10-19 & 10 \\\hline 20-29 & 5 \\\hline 30-39 & 9 \\\hline 40-49 & 6 \\\hline 50-59 & 7 \\\hline 60-69 & 1 \\\hline\end{tabular}

### Example 3: For the following data showing weights of toffee boxes in gm. Determine the modal weight of boxes.\begin{tabular}{|c|c|}\hline Classes / Groups & Frequency \\\hline 0-9 & 2 \\\hline 10-19 & 10 \\\hline 20-29 & 5 \\\hline 30-39 & 9 \\\hline 40-49 & 6 \\\hline 50-59 & 7 \\\hline 60-69 & 1 \\\hline\end{tabular}

5. a- Find the standard deviation " S " of each set of numbers:(i) 126731510185

### 5. a- Find the standard deviation " S " of each set of numbers:(i) 126731510185

Example 1: The following table gives the monthly earnings and the number of workers in a factory compute the weighted average.\begin{tabular}{|c|c|}\hline No. of employees & Monthly earnings. Rs. \\\hline 4 & 800 \\22 & 45 \\20 & 100 \\30 & 30 \\80 & 35 \\300 & 15 \\\hline\end{tabular}

### Example 1: The following table gives the monthly earnings and the number of workers in a factory compute the weighted average.\begin{tabular}{|c|c|}\hline No. of employees & Monthly earnings. Rs. \\\hline 4 & 800 \\22 & 45 \\20 & 100 \\30 & 30 \\80 & 35 \\300 & 15 \\\hline\end{tabular}

2 . Define Arithmetic mean Geometric mean Harmonic mean mode and median.

### 2 . Define Arithmetic mean Geometric mean Harmonic mean mode and median.

9. The following frequency distribution the weights of boys in kilogram. Compute mean median mode.\begin{tabular}{|c|c|}\hline Class Intervals & Frequency \\\hline 1-3 & 2 \\\hline 4-6 & 3 \\\hline 7-9 & 5 \\\hline 10-12 & 4 \\\hline 13-15 & 6 \\\hline 16-18 & 2 \\\hline 19-21 & 1 \\\hline\end{tabular}

### 9. The following frequency distribution the weights of boys in kilogram. Compute mean median mode.\begin{tabular}{|c|c|}\hline Class Intervals & Frequency \\\hline 1-3 & 2 \\\hline 4-6 & 3 \\\hline 7-9 & 5 \\\hline 10-12 & 4 \\\hline 13-15 & 6 \\\hline 16-18 & 2 \\\hline 19-21 & 1 \\\hline\end{tabular}

Example 2: Calculate three days moving average for the following record of attendance:\begin{tabular}{|c|c|c|c|c|c|c|c|}\hline Week & Sun & Mon & Tue & Wed & Thu & Fri & Sat \\\hline 1 & 24 & 55 & 28 & 45 & 51 & 54 & 60 \\\hline\end{tabular}

### Example 2: Calculate three days moving average for the following record of attendance:\begin{tabular}{|c|c|c|c|c|c|c|c|}\hline Week & Sun & Mon & Tue & Wed & Thu & Fri & Sat \\\hline 1 & 24 & 55 & 28 & 45 & 51 & 54 & 60 \\\hline\end{tabular}

3. Find arithmetic mean by direct method for the following set of data:(i) 1214172024293545 .

### 3. Find arithmetic mean by direct method for the following set of data:(i) 1214172024293545 .

Example 2: Find Mode for the following frequency distribution.\begin{tabular}{|c|c|}\hline (Number of heads) X & Frequency \\\hline 1 & 3 \\\hline 2 & 8 \\\hline 3 & 5 \\\hline 4 & 3 \\\hline 5 & 1 \\\hline\end{tabular}

### Example 2: Find Mode for the following frequency distribution.\begin{tabular}{|c|c|}\hline (Number of heads) X & Frequency \\\hline 1 & 3 \\\hline 2 & 8 \\\hline 3 & 5 \\\hline 4 & 3 \\\hline 5 & 1 \\\hline\end{tabular}

(xviii) The spread or scatterness of observations in a data set is called(a) average(b) dispersion(c) central tendency

### (xviii) The spread or scatterness of observations in a data set is called(a) average(b) dispersion(c) central tendency

1. The following data shows the number of members in various families. Construct frequency distribution. Also find cumulative frequencies.\[\begin{array}{l}911456843785583491289106771144843279 \\10976957 .\end{array}\]

### 1. The following data shows the number of members in various families. Construct frequency distribution. Also find cumulative frequencies.\[\begin{array}{l}911456843785583491289106771144843279 \\10976957 .\end{array}\]

Example 3: Compute class boundaries class marks and cumulative frequency for data of example 2 .

### Example 3: Compute class boundaries class marks and cumulative frequency for data of example 2 .

(xi) Mean is affected by change in(a) place(b) scale(c) rate

### (xi) Mean is affected by change in(a) place(b) scale(c) rate

Example 2: The salaries of five teachers are as follows. Find the mean salary using direct and indirect methods and compare the results. 1150012400150001450014800 .

### Example 2: The salaries of five teachers are as follows. Find the mean salary using direct and indirect methods and compare the results. 1150012400150001450014800 .

4. The following data shows the daily load shedding duration in hours in 30 localities of a certain city. Make a frequency distribution of the load shedding duration taking 2 hours as class interval size and answer the following questions. 612578367102141112868971169121310147610 111412 . (b) Find the least load shedding intervals?(Hint: Make classes 2-34-56-7 \ldots )

### 4. The following data shows the daily load shedding duration in hours in 30 localities of a certain city. Make a frequency distribution of the load shedding duration taking 2 hours as class interval size and answer the following questions. 612578367102141112868971169121310147610 111412 . (b) Find the least load shedding intervals?(Hint: Make classes 2-34-56-7 \ldots )

2. Write short answers of the following questions.(xiv) Define Standard deviation.

### 2. Write short answers of the following questions.(xiv) Define Standard deviation.

2. Write short answers of the following questions.(vii) Define Arithmetic mean.

### 2. Write short answers of the following questions.(vii) Define Arithmetic mean.

4. The following data shows the daily load shedding duration in hours in 30 localities of a certain city. Make a frequency distribution of the load shedding duration taking 2 hours as class interval size and answer the following questions. 612578367102141112868971169121310147610 111412 .(a) Find the most frequent load shedding hours?

### 4. The following data shows the daily load shedding duration in hours in 30 localities of a certain city. Make a frequency distribution of the load shedding duration taking 2 hours as class interval size and answer the following questions. 612578367102141112868971169121310147610 111412 .(a) Find the most frequent load shedding hours?

Example 1: Find Range for the following weights of students: 1101098489771047497495910362 .

### Example 1: Find Range for the following weights of students: 1101098489771047497495910362 .

Example 3: Find median for the following frequency distribution.\begin{tabular}{|c|c|}\hline (Number of heads) X & Frequency \\\hline 1 & 3 \\\hline 2 & 8 \\\hline 3 & 5 \\\hline 4 & 3 \\\hline 5 & 1 \\\hline\end{tabular}

### Example 3: Find median for the following frequency distribution.\begin{tabular}{|c|c|}\hline (Number of heads) X & Frequency \\\hline 1 & 3 \\\hline 2 & 8 \\\hline 3 & 5 \\\hline 4 & 3 \\\hline 5 & 1 \\\hline\end{tabular}

10. A student obtained the following marks at a certain examination: English 73 Urdu 82 Mathematics 80 History 67 and Science 62 .(i) If the weights accorded these marks are 4332 and 2 respectively what is an appropriate average mark?

### 10. A student obtained the following marks at a certain examination: English 73 Urdu 82 Mathematics 80 History 67 and Science 62 .(i) If the weights accorded these marks are 4332 and 2 respectively what is an appropriate average mark?

Example 1: Find the mean of observations: 343434343434 .