Frequency Distribution

Frequency distribution is arrangement of data in a table format where each entry displays the frequency of occurrence of each of the values.

A frequency distribution of data can be represented in the form of frequency tables, histograms or bar charts.

Example:

Grade 5 has 9 students and last week they got their math performance report. The scores obtained were:

90, 80, 60, 20, 40, 50, 70, 90

The frequency distribution table for the above data will be:

Scores Tally marks Frequency(f)
90 || 2
80 | 1
60 | 1
20 | 1
40 | 1
50 | 1
70 | 1

Grouped Frequency Distribution

Steps to determine frequency distribution:

• 1. Find the maximum and minimum values. Write the values in the variable column, starting from minimum to maximum.
• 2. Find the frequency of each value using tally marks (a vertical bar denoted by '|').
• 3. Count the number of tally marks to find the frequency of each variable.Write down the frequency in the frequency column.

Flipping a coin

6 coins were tossed 25 times. Determine the frequency at which the coin should land heads-up every time.
The frequency of heads were: 3, 4, 3, 2, 5, 2, 2, 6, 2, 4, 4, 1, 3, 1, 2, 2, 5, 3, 6, 5, 4, 4, 3, 6, 2

Explanation:

1. Determine the minimum and maximum values.

Here,

Minimum value is 1

Maximum value is 6

2. Use tally marks to record the frequency of heads.

No. of coins tossed Tally Marks Frequency of heads
1 ||
2 |||| |||
3 |||| |
4 |||| |
5 |||
6 |||

3. Count the tally marks to find the frequency of heads.

No. of coins tossed Tally Marks Frequency of heads
1 || 2
2 |||| ||| 7
3 |||| | 5
4 |||| | 5
5 ||| 3
6 ||| 3

People of different age groups

You are given a file that shows age record of 40 people living in an apartment complex. Classify them into 10 different age groups and create a frequency distribution table.
The ages are as follows:
43, 34, 18, 56, 7, 28, 23, 49, 62, 51, 12, 21, 34, 47, 40, 57, 29, 25, 36, 54, 4, 35, 27, 39, 15, 20. 67, 35, 48, 41, 14, 52, 40, 25, 30, 33, 44, 17, 11, 37

Explanation:

1. Find the minimum and maximum value

Here,

Minimum value is 4

Maximum value is 67

2. Calculate the range

Range=Maximum- Minimum

67 - 4 = 63

The range is 63

3. Calculate group size.

Divide the range by number of groups, then round up that group size

So, 64/10 is 6.4

6.4 rounded to its nearest integer value (that is greater than 6.4) is 7

4. Select a starting value.

Choose the lowest number from the group or select 0.

5. Form groups.

Create a list of groups and put them in the first column, which is the data groups or class intervals.Make sure the end value of each group is less than the start value of the next group.

Class Intervals Tally Marks Frequency of heads
0-9
10-19
20-29
30-39
40-49
50-59
60-69

6. Get the upper and lower limits for each group.

7. Use tally marks to record the observations.

Class Intervals Tally Marks Frequency of heads
0-9 ||
10-19 |||| ||
20-29 |||| ||||
30-39 |||| |||| |
40-49 |||| ||||
50-59 |||| |
60-69 ||

8. Count the tally marks for each group.

After counting, write the corresponding frequency in the frequency column.

Class Intervals Tally Marks Frequency of heads
0-9 || 2
10-19 |||| || 6
20-29 |||| |||| 8
30-39 |||| |||| | 9
40-49 |||| |||| 8
50-59 |||| | 5
60-69 || 2

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