Unit 2 question

1. Find the median score of 7 students in science class

Solution

Score = 19, 17, 16, 15, 12, 11, 10

Median = (7+1)/2 = 4th value

Median = 15

2.      find the median of the table given below

Solution

Median = (n+1)/2 = 100+1/2 = 50.5

Median = (28+29)/2 = 28.5

3.      Calculate the median

Solution

n = 50

n         = 50/2= 25

2

The category containing n/2 is 15 -19

Lb = 15

Cfp = 24

f = 17

Ci = 4

Median = 15 + 25-24 *4 = 15.23

  17

4.      In a class of 30 students marks obtained by students in science out of 50 is tabulated below. Calculate the mode of the given data.

Solution

The group with the highest frequency is the modal group: - 20 -30

D1 = 12 - 5 = 7

D2 = 12 - 8 = 4

Mode = L1 + (L2 – L1)   d1

                                       d1 +d2

mode  = 20 + (30-20)  7         = 20+10 (7/11) = 26.36

7+4

Mode = 61.8

5.      The following data represent the income distribution of 100 families. Calculate mean income of 100 families?

Solution

X  = ∑f Xm/n = 6330/100 = 63.30

Mean = 63.30

6.      calculate the geometric mean

Solution

GM = Antilog ∑ f logxi

     N

= antilog 280.68/140

= antilog 2.00

     GM = 100

7.      calculate harmonic mean

Solution

Harmonic mean = 10/2.19 = 4.55

8.     Compute 5-year, 7-year and 9-year moving averages for the following data.

Solution

9.     Compute 4-year moving averages centered for the following time series:

Solution

10. For a moderately skewed distribution , the median is 20 and the mean is 22.5. Using these values, find the approximate value of the mode.

Solution:

Given,

Mean = 22.5

Median = 20

Mode = x

Now, using the relationship between mean mode and median we get,

(Mean – Mode) = 3 (Mean – Median)

So,

22.5 – x = 3 (22.5 – 20)

22.5 – x = 7.5

∴ x = 15

So, Mode = 15.