Download Tutorial Sheet 1

Department of Mathematics
MAL 108 (Introduction to Statistics)
Tutorial Sheet No. 1 (Descriptive Statistics)
1. The following is a sample of prices of Basmati rice per 2 Kg in the Delhi in July 2015.
157, 159, 161, 157, 164, 161, 159, 157, 164, 161, 163, 163, 161
Represent these data in
(a) a frequency table.
(b) a relative frequency line graph
2. Marks obtained by a class of students (out of 100) in course MTL108: Introduction to statistics
are as follows:
68 34 56 23 45 78 67 96 76 45 75 34 89 92 50 47 56
53 19 45 34 23 76 45 67 43 56 78 94 74 38 58 52 64
72 59 55 92 88 53 71 49 53 89 48 58 54 39 66 62
(a) Write the frequency table for interval of ten marks i.e. 1-10, 11-20 and so on.
(b) Draw the histogram of the distribution.
(c) Comment on the symmetry and peakedness of the distribution after calculating appropriate
measures (skewness and Kurtosis).
(d) Determine the proportion of the data values that lies within x̄1.5s.
3. A mobile phone company examines the ages of 150 customers to start special plans for them. The
Frequency table is as follows:
Age(years)
Frequency
0-14
14
15-19
40
20-29
28
30-39
27
40-49
24
50-79
17
(a) Draw the histogram for the data.
(b) Estimate the mean age for these policyholders.
(c) Estimate the median age for these policyholders.
(d) Calculate inter-quartile range.
4. A sample of 10 claims in an insurance company had mean and variance of 5,478 and 1,723 respectively. On reconciliation, it was found that one claim of 3,250 was wrongly written as 4,250.
Calculate the sample mean and standard deviation of the sample with correct values.
5. Government of Tamilnadu wants to analyze the number of children in families for improving their
immunization program. They analyze a group of 200 families and report their findings in the form
of a frequency distribution shown below:
No. of children
No of families
0
18
1
30
1
2
72
3
43
4
25
5
8
6
3
7
1
(a) Draw the bar chart for the following data and calculate the total number of children.
(b) Calculate mean, mode and median of the data.
(c) Calculate sample mean, sample variance and coefficient of variation of the data.
(d) Calculate Coefficient of kurtosis and Coefficient of skewness in the above data.
6. An insurance company wants to analyze the claims for damage due to fire on its household content’s
policies. Following are the values for a sample of 50 claims in Rupees.
57000, 115000, 119000, 131000, 152000, 167000, 188000, 190000, 197000,
201000, 206000, 209000, 213000, 217000, 221000, 229000, 247000, 250000,
252000, 253000, 257000, 257000, 258000, 259000, 260000, 261000, 262000,
263000, 267000, 271000, 277000, 285000, 287000, 305000, 307000, 309000,
311000, 313000, 317000, 321000, 322000, 327000, 333000, 351000, 357000,
371000, 399000, 417000, 433000, 499000
The table given below displays the grouped frequency distribution for the above data.
Claim Size(In 1000’s of Rupees)
Frequency
50-99
100-149
150-199
200-249
250-299
300-349
350-399
400-449
450- 500
1
3
5
8
16
10
4
2
1
(a) What is the range of the above data?
(b) Draw a bar graph for the above data
(c) For the data given above if instead of equal sized groups we had a single group for all value
below 250, how would this bar be represented?
(d) Calculate the mean, median and mode for the above data.
(e) Calculate the sample geometric mean.
(f) Calculate the sample standard deviation and sample variance.
(g) Calculate the coefficient of variation for the above data.
7. An experiment measuring the percent shrinkage on drying of 50 clay specimens produced the
following data:
18.2 21.2 23.1 18.5 15.6 20.8 19.4 15.4 21.2 13.4
16.4 18.7 18.2 19.6 14.3 16.6 24.0 17.6 17.8 20.2
2
17.4 23.6 17.5 20.3 16.6 19.3 18.5 19.3 21.2
20.5 19.0 17.6 22.3 18.4 21.2 20.4 21.4 20.3
19.6 20.6 14.8 19.7 20.5 18.0 20.8 15.8 23.1
Group the data into class intervals of size
togram. Also, find the
13.9
20.1
17.0
1 percent starting with the value 13.0. Draw the his-
(a) 10 percentile of the median prices;
(b) 40 percentile of the median prices;
(c) 90 percentile of the median prices
8. The sample mean and sample variance of five data values are, respectively, x̄ = 104 and s2 = 8.5.
If three of the data values are 102, 100, 105, what are the other two data values?
9. Explain how a pie chart can be constructed. If a data value had relative frequency r, at what angle
would the lines defining its sector meet?
10. Pearson’s measure of skewness of a distribution is 0.5. Its median and mode are 42 and 36 respectively. Find the coefficient of variation.
11. Compute the coefficient of Quartile deviation of the following data
Size
Frequency
4-8
6
8-12
10
12-16
18
16-20
30
20-24
15
24-28
12
28-32
10
32-26
6
36-40
2
12. Calculate mean deviation from median of the following data
Class Interval
Frequency
50-100
7
100-150
18
150-200
25
3
200-250
31
250-300
15
300-350
4