1 Marks Question

Question 11 Mark

Consider the following frequency distribution:

Class	0-5	6-11	12-17	18-23	24-29
Frequency	13	10	15	8	11

Find the upper limit of the median class.

Answer

The given series is in indusive from. Converting it to exclusive from and preparing cumulative frequency table, we get

Class	Frequency	Cumulative frequency
0.5-5.5	13	13
5.5-11.5	10	23
11.5-17.5	15	38
17.5-23.5	8	46
23.5-29.5	11	57

Here, $\text{N}=57\Rightarrow\frac{\text{N}}{2}=28.5$
The cumulative frequency just greater than 28.5 is 38.
Hence, the median class is 11.5-17.5
$\therefore$ Upper limit of the median class = 17.5

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Question 21 Mark

If the mean and mode of a frequency distribution be 53.4 and 55.2 respectively, find the median.

Answer

Mean = 53.4
Mode = 55.2
Mode = 3Median - Mean
Hence, median = $\frac{\text{Mode}+2\text{Mean}}{3}$
$=\frac{55.2+2(53.4)}{3}$
$=\frac{55.2+106.8}{3}$
$=\frac{162}{3}$
$=54$

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Question 31 Mark

The annual profit earned by 30 shops of a shopping complex in a locality are recorded in the table shown below:

Profit (in lakhs Rs.)	Number of shops
More than or equal to 5	30
More than or equal to 10	28
More than or equal to 15	16
More than or equal to 20	14
More than or equal to 25	10
More than or equal to 30	7
More than or equal to 35	3

If we draw the frequency distribution table for the above data, find the frequency corresponding to the class 20-25.

Answer

The frequency table is as follows:

Classes Profit (in lakhs Rs.)	frequency Number of shops
5-10	2
10-15	12
15-20	2
20-25	4
25-30	3
30-35	4
35-40	4

Thus, the frequency corresponding to the class 20-25 is 4.

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Question 41 Mark

In the table given below, the times taken by 120 athletes to run a 100 m hurdle race are given:

Class	13.8-14	14-14.2	14.2-14.4	14.4-14.6	14.6-14.8	14.8-15
Frequency	2	4	15	54	25	20

Find the number of athletes who completed the race in less than 14.6 seconds.

Answer

Number of athletes who completed the race in less than 14.6 seconds
= 2 + 4 + 15 + 54
= 75

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