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9.   The following table gives the literacy rate (in percentage) of 35 cities. Find the mean  literacy rate.

Let the assumed mean be a = 75 and h = 10 Literacy rates   Number of cities  Class mark 45-55 3 50 -20 -2 -6 55-65 10 60 -10 -1 -10 65-75 11 70 0 0 0 75-85 8 80 10 1 8 85-95 3 90 20 2 6   = 35       = -2 Mean,    Therefore, the mean mean literacy rate is 69.43%

8.  A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days Number of Students  Class mark 0-6 11 3 33 6-10 10 8 80 10-14 7 12 84 14-20 4 17 68 20-28 4 24 96 28-38 3 33 99 38-40 1 39 39             =40   =499 Mean,  Therefore, the mean number of days a student was absent is 12.48 days.

7. To find out the concentration of $SO_2$ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

Find the mean concentration of $SO_2$ in the air.

Class  Interval Frequency  Class mark 0.00-0.04 4 0.02 0.08 0.04-0.08 9 0.06 0.54 0.08-0.12 9 0.10 0.90 0.12-0.16 2 0.14 0.28 0.16-0.20 4 0.18 0.72 0.20-0.24 2 0.22 0.44     =30   =2.96 Mean,  Therefore, the mean concentration of in the air is 0.099 ppm

6.  The table below shows the daily expenditure on food of 25 households in a locality.

Find the mean daily expenditure on food by a suitable method.

Let the assumed mean be a = 225 and h = 50 Daily Expenditure   Number of households  Class mark 100-150 4 125 -100 -2 -8 150-200 5 175 -50 -1 -5 200-250 12 225 0 0 0 250-300 2 275 50 1 2 300-350 2 325 100 2 4   =25       = -7 Mean,    Therefore, the mean daily expenditure on food is Rs. 211

5.   In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Let the assumed mean be a = 57

 Number of  mangoes Number of boxes $f_i$ Class mark $x_i$ $d_i = x_i -a$ $f_id_i$ 50-52 15 51 -6 -90 53-55 110 54 -3 -330 56-58 135 57 0 0 59-61 115 60 3 345 62-64 25 63 6 150 $\sum f_i$  =400 $\sum f_ix_i$ =75

Mean,

$\overline x =a + \frac{\sum f_id_i}{\sum f_i}$
$= 57+ \frac{75}{400} = 57+0.1875 = 57.1875 \approx 57.19$
Therefore, the mean number of mangoes kept in a packing box is approx 57.19

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4.   Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.

Let the assumed mean be a = 75.5

 No. of heartbeats per minute Number of women $f_i$ Class mark $x_i$ $d_i = x_i -a$ $f_id_i$ 65-68 2 66.5 -9 -18 68-71 4 69.5 -6 -24 71-74 3 72.5 -3 -9 74-77 8 75.5 0 0 77-80 7 78.5 3 21 80-83 4 81.5 6 24 83-86 2 84.5 9 18 $\sum f_i$ =30 $\sum f_ix_i$ =12

Mean,

$\overline x =a + \frac{\sum f_id_i}{\sum f_i}$
$= 75.5 + \frac{12}{30} = 75.5 + 0.4 = 75.9$
Therefore, the mean heartbeats per minute of these women is 75.9

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3.   following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.

Daily pocket allowance Number of children  Class mark 11-13 7 12 84 13-15 6 14 84 15-17 9 16 144 17-19 13 18 234 19-21 f 20 20f 21-23 5 22 110 23-25 4 24 96     =44+f   =752+20f Mean,  Therefore the missing f = 20

2.   Consider the following distribution of daily wages of 50 workers of a factory.

Find the mean daily wages of the workers of the factory by using an appropriate method.

Let the assumed mean be a = 550 Daily  Wages    Number of workers  Class mark 500-520 12 510 -40 -480 520-540 14 530 -20 -280 540-560 8 550 0 0 560-580 6 570 20 120 580-600 10 590 40 400     =50     =-240 Mean,  Therefore, the mean daily wages of the workers of the factory is Rs. 545.20

1. A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Which method did you use for finding the mean, and why?

Number of plants   Number of houses     Class mark 0-2 1 1 1 2-4 2 3 6 4-6 1 5 5 6-8 5 7 35 8-10 6 9 54 10-12 2 11 22 12-14 3 13 39     =20   =162 Mean,  We used the direct method in this as the values of are small.
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