# Class 10 Math Basic Statistics 2. How do you define measures of dispersion?

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##### 2. How do you define measures of dispersion?

(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

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}

(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.

(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}

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}

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}

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 .

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

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 .

(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 .

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.(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?

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}

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 .