Objective
Analysis of a language text, using graphical and pie chart techniques. How to Proceed
1. Students should select any paragraph containing approximately 300 words from any source. e.g., newspaper, magazine, textbook, etc.
2. Now read every word and obtain a frequency table for each letter of the alphabet as follows: Table – 1
Letter Tally Marks Frequency
A B C . . . . Z
3. Note down the number of two-letter words, three-letter words, so on and obtain a frequency table as follows: Table – 2
Number of Words With Tally Marks Frequency
2 Letter 3 Letter . . . . . Investigate the following: From Table 1
1. What is the most frequently occurring letter? 2. What is the least frequently occurring letter? 3. Compare the frequency of vowels.
4. Which vowel is most commonly used? 5. Which vowel has the least frequency?
6. Make a pie chart of the vowels a, e, i, o, u and remaining letters. (The pie chart will thus have 6 sectors.) 7. Compare the percentage of vowels with that of consonants in the given text.
From Table 2
1. Compare the frequency of two letter words, three letter words, ... and so on. 2. Make a pie chart. Note any interesting patterns.
Seminar
Students should make presentations on following topics and discuss them in the class in the presence of teachers.
1. Different types of graphical presentation of data, with examples from daily life (may use news paper cuttings also).
2. Measures of central tendency.
3. Why do we need deviation and step deviation methods?
Multiple Choice Questions
Tick the correct answer for each of the following:
1. While computing mean of a grouped data, we assume that the frequencies are
(a) centered at the lower limits of the classes (b) centered at the upper limits of the classes (c) centered at the class marks of the classes (d) evenly distributed over all the classes. 2. The graphical representation of a cumulative frequency distribution is called
3. Construction of a cumulative frequency table is useful in determining the
(a) mean (b) median (c) mode (d) all of the above 4. The class mark of the class 15.5–20.5 is
(a) 15.5 (b) 20.5 (c) 18 (d) 5
5. If xi’s are the mid-points of the class intervals of a grouped data fi’ s are the corresponding frequencies and x is the mean, then Σ(f xi i −x) is equal to
(a) 0 (b) –1 (c) 1 (d) 2 6. In the formula, Mode = l f f
f f f h i o o + − − − 2 × 1 2 , f2 is (a) frequency of the modal class
(b) frequency of the second class
(c) frequency of the class preceding the modal class (d) frequency of the class succeeding the modal class 7. Consider the following distribution:
Marks Obtained Number of Students
Less than 10 5 Less than 20 12 Less than 30 22 Less than 40 29 Less than 50 38 Less than 60 47 The frequency of the class 50–60 is
(a) 9 (b) 10 (c) 38 (d) 47 8. For the following distribution:
Class 0–8 8–16 16–24 24–32 32–40
Frequency 12 26 10 9 15
The sum of upper limits of the median class and modal class is
(a) 24 (b) 40 (c) 32 (d) 16 9. Consider the following distribution:
Marks Number of Students
More than or equal to 0 53 More than or equal to 20 51 More than or equal to 40 45 More than or equal to 60 37 More than or equal to 80 25
The modal class is
(a) 80–100 (b) 60–80 (c) 40–60 (d) 0–20 10. Consider the following frequency distribution:
Class 0–15 15–30 30–45 45–60 60–75
Frequency 15 12 18 16 9
The difference of the upper limit of the median class and the lower limit of the modal class is (a) 0 (b) 15 (c) 10 (d) 5
11. The runs scored by a batsman in 35 different matches are given below:
Runs Scored 0–15 15–30 30–45 45–60 60–75 75–90
Number of Matches 5 7 4 8 8 3
The number of matches in which the batsman scored less than 60 runs are (a) 16 (b) 24 (c) 8 (d) 19
Rapid Fire Quiz
State which of the following statements are true (T) or false (F).
1. The mean, median and mode of a data can never coincide. 2. The modal class and median class of a data may be different.
3. An ogive is a graphical representation of a grouped frequency distribution. 4. An ogive helps us in determining the median of the data.
5. The median of ungrouped data and the median calculated when the same data is grouped are always the same.
6. The ordinate of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its median.
7. While computing the mean of grouped data, we assume that the frequencies are centered at the class marks of the classes.
8. A cumulative frequency table is useful in determining the mode.
9. The value of the mode of a grouped data is always greater than the mean of the same data.
Match the Columns
Consider the following distribution:
Height (cm) Number of Students
135–140 3 140–145 9 145–150 22 150–155 15 155–160 8 160–165 5 165–170 2
On the basis of the above data, match the following columns:
Column I Column II
(i) Lower limit of median class (a) 12 (ii) Upper limit of modal class (b) 57 (iii) Number of students with heights less than 160 cm (c) 5 (iv) Number of students with heights more than or equal
to 150 cm
(d) 145 (v) Number of students in the median class (e) 150 (vi) Cumulative frequency of the class preceding the
modal class
(f) 15 (vii) Class size (g) 30 (viii) Number of students in the class succeeding the modal
class
(h) 22
Group Discussion
Divide the whole class into small groups and ask them to discuss the choice of different measures of central tendency in different situations, i.e., which measure is more appropriate in a given situation.
The situations may include, finding average income, putting shirts of different sizes in a shop, dividing a group in two parts on the basis of the heights of members of group, etc.
(Note: The students may discuss it on the basis of the activities done by them.)
Project Work
Objective
To apply the knowledge of statistics in real life.
Form group of students with about 5-8 students in each group. Each group is supposed to work as a team for the completion of project. Some members can take responsibility of gathering required information for the project, other students can work for making a rough draft from the collected information. All members of the group should discuss the draft and give inputs for final presentation. After finalizing, few members can write the report.