Question

Class 0.5 – 5.5 5.5 – 10.5 10.5 – 15.5 15.5 – 20.5 20.5-2 22 18 11 Frequency 13 16 The mean of the above data is (a) 13.9 (b) 12.9 (c) 11.9 (d) 14.9 T ​

Answer 1

Step-by-step explanation:

Answer:

The cumulative frequency Table is:

Class Frequency Cumulative frequency

0-5

10

5-10 15

10-15 12

15-20 20

20-25 9

10

25

37

57

66

N 2 66 2 Here, 33

Thus 37 is just greater than 33, ...The median class is "10 15."

The lower limit of the median class is 10. Modal class = class with maximum frequency.

...Modal class is 15 - 20.

The lower limit of the modal class is 15. Sum of lower limits of median class and modal class = 10 + 15 = 25

Answer 2

Answer: (b) 12.9

Solution:

Formula:

The mean of the data is given by the ratio of the sum of all the data points to the total number of observed data points.

The average mean is given by:

$X = \frac{Sum (X_i * f_i) }{Sum(f_i)}$ ......................... (1)

Where Xi is the individual mean of each class and fi is the individual frequency of each class.

The value of individual mean Xi can be calculated by using the formula,

$X_i = \frac{l_1 + l_2}{2}$,

where l1 and l2 are the lower and upper limit of the given class respectively.

for X1 Calculations:

Xi = (0.5 + 5.5)/ 2 = 6/2 = 3

Similarly all the values are calculated.

The Class and the frequency table along with the calculated values of Xi, fi, and Xi*fi  are shown in the figure.

Putting the values of the sum of Xi*fi   and Sum of fi in equation 1,

X = 1030/80

X= 12.9

Hence the correct answer is (b) 12.9

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