**1.** Since, number of plants and houses are small in their values, so we use direct method.

Hence mean number of plants per house is 8.1.

From given data, Assume mean *(a) = *150, Width of the class *(h) = *20

Hence mean daily wages of the workers of factory is Rs.145.20.

From given data, Assume mean *(a) = *18

Hence missing frequency is 20.

From given data, Assume mean *(a) = *75.5, Width of the class *(h) = *3

Hence mean heart beat per minute for women is 78.89.

**5.** Since value of number of mangoes and number of boxes are large numerically. So we use step-deviation method.

From given data, Assume mean *(a) = *57, Width of the class *(h) = *3

Hence mean number of mangoes kept in a packing box is 57.19.

From given data, Assume mean *(a) = *225, Width of the class (11) = 50

Hence mean daily expenditure on food is Rs.211.

From given data, Assume mean *(a) = *0.10, Width of the class *(h) = *0.04

Hence mean concentration of ^{so2} in air is 0.0987 ppm.

From given data, Assume mean *(a) = *17

Hence mean 12.48 number of days a student was absent.

From given data, Assume mean *(a) = *70, Width of the class *(h*) = 10

Hence mean literacy rate is 69.43%.

**10.** **For Mode : **In the given data, maximum frequency is 23 and it corresponds to the class interval 35 – 45.

From given data, Assume mean *(a) = *30, Width of the class *(h) = *10

Using formula, Mean * = *30 + 10 (0.5375) = 30 + 5.375 = 35.37

Hence mode of given data is 36.8 years and mean of the given data is 35.37 years.

Also, it is clear from above discussion that average age of a patient admitted in the hospital is 35.37 years and maximum number of patients admitted in the hospital are of age 36.8 years.

**11. ** Given: Maximum frequency is 61 and it corresponds to the class interval 60 – 80.

∴ Modal class = 60 – 80

And *l* = 60, *f*_{1} *= *61, *f*_{0} =52, *f*_{2} = 38 and *h = *20

Hence modal lifetimes of the components is 65.625 hours.

**12.** **For Mode : **Here, Maximum frequency is 40 and it corresponds to the class interval 1500 – 2000

∴ Modal class = 1500 – 2000

And *l* = 1500, *f*_{1} = 40, *f*_{0} = 24, *f*_{2} = 33 and *h* = 500

From given data, Assume mean *(a) = *2750, Width of the class *(h) = *500

Using formula, Mean *= *2750 + 500 (- 0.175) = 2750 – 87.50 = 2662.50

Hence the modal monthly expenditure of family is Rs.1847.83 and the mean monthly expenditure is Rs.2662.50.

**13.** **For Mode : **Here, Maximum frequency is 10 and it corresponds to the class interval 30 – 35.

∴ Modal class = 30 – 35

And *l* = 30, *f*_{1} = 10, *f*_{0} = 9, *f*_{2} = 3 and *h* = 5

From given data, Assume mean *(a) = *32.5, Width of the class *(h) = *5

Using formula, Mean *= *32.5 + 5 (- 0.65) = 32.5 – 3.25 = 29.25 (approx.)

Hence mode and mean of given data is 30.63 and 29.25. Also from above discussion, it is clear that states/U.T. have students per teacher is 30.63 and on average, this ratio is 29.25.

**14.** In the given data, maximum frequency is 18 and it corresponds to the class interval 4000 -5000.

∴ Modal class = 4000 – 5000

And *l* = 400, *f*_{1} = 18, *f*_{0} = 4, *f*_{2} = 9 and *h* = 1000

Hence, mode of the given data is 4608.7 runs.

**15. ** In the given data, maximum frequency is 20 and it corresponds to the class interval 40 – 50.

∴ Modal class = 40 – 50

And *l* = 40, *f*_{1} = 20, *f*_{0} = 12, *f*_{2} = 11 and *h* = 10

Hence, mode of the given data is 44.7 cars.

**16.** **For Median:**

Here, which lies in interval 125 – 145.

**For Mean:**

From given data, Assume mean *(a) = *135, Width of the class *(h) *= 20

Using formula, Mean *= *135 + 20 (0.102) = 135 + 2.04 = 137.04

**For Made:**

In the given data, maximum frequency is 20 and it corresponds to the class interval 125 – 145.

∴ Modal class = 125 – 145

And *l* = 125, *f*_{1} = 20, *f*_{0} = 13, *f*_{2} = 14 and *h* = 20

Hence, median, mean and mode of given data is 137 units, 137.04 units and 135.77 units.

Here, , also median of the distribution is 28.5,which lies interval 20 – 30.

Hence the value of x and *y *is 8 and 7 respectively.

Here, which lies in interval 35 – 40.

∴ Modal class = 35 – 40

And *l* = 35, *n* = 100, *f* = 33, *cf* = 45 and *h* = 5

Hence median age of given data is 35.76 years.

**19.** Since the frequency distribution is not continuous, so firstly we shall make it continuous.

Here, which lies in interval 144.5 – 153.5.

∴ Modal class = 144.5 – 153.5

So, *l* = 144.5, *n* = 40, *f* = 12, *cf* = 17 and *h* = 9

Hence median length of the leaves is 146.75 mm.

Here, , which lies in interval 3000 – 3500.

∴ Modal class = 3000 – 3500

So, *l* = 3000, *n* = 400, *f* = 86, *cf* = 130 and *h* = 500

Hence median life time of a lamp is 3406.98 hours.

**21. ** **For Median:**

Here, which lies in interval 7 – 10.

∴ Modal class = 7 – 10

So, *l* = 7, *n* = 100, *f* = 40, *cf* = 36 and *h* = 3

**For Mean:**

From given data, Assume mean *(a) = *8.5, Width of the class *(h) = *3

Using formula, Mean = * *8.5 + 3 (- 0.06) = 8.5 – 0.18 = 8.32

**For Mode:**

In the given data, maximum frequency is 40 and it corresponds to the class interval 7 – 10.

∴ Modal class = 7 – 10

And *l* = 7, *f _{1}* = 40,

*f*= 30,

_{0}*f*= 16 and

_{2}*h*= 3

Hence, median, mean and mode of given data is 8.05 letters, 8.32 letters and 7.88 letters respectively.

Here, , which lies in interval 55 – 60.

∴ Modal class = 55 – 60

So, *l* = 55, *n* = 30, *f* = 6, *cf* = 13 and *h* = 5

Hence median weight of the students are 56.67 kg.

Now, by drawing the points on the graph,

i.e., (120, 12); (140, 26); 160, 34); (180, 40); (200, 50)

Scale: On x – axis 10 units = Rs.10 and on y – axis 10 units = 5 workers

Hence, the points for graph are:

(38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32), (52, 35)

Scale: On *x-axis, *10 units = 2 kg and on y-axis, 10 units = 5 students

From the above graph, Median = 46.5 kg, which lies in class interval 46 – 48.

Here, which lies in interval 46 – 48.

∴ Modal class = 55 – 60

So, *l* = 46, *n* = 35, *f* = 14, *cf* = 14 and *h* = 2

Hence median weight of students is 46.5 kg.

The points for the graph are:

(50, 100), (55, 98), (60, 90), (65, 78), (70, 54), (75, 16)

Scale: On x- axis, 10 units = 5 kg/ha and on y-axis, 10 units = 10 forms.