**Grouping data in intervals :**

Once the data is selected, it has to be presented in a neat and precise manner such that any one can understand.

To present the date in a neat and precise manner, we have to group the data in intervals.

**Example 1 :**

The members of the high-school basketball team practice free throws. Each player attempts 50 free throws. The number of free throws made by each player is listed below.

25, 29, 29, 30, 33, 34, 35, 35, 36, 39, 42, 44

(i) Use a dot plot to represent the data.

(ii) On your dot plot, circle the dots that are in each interval of the frequency table below. Then complete the frequency table.

(iii) Analyze the data. How were the data collected ? How many data values are there ? What are the mean, median, range, and IQR of the data ?

**Solution (i) :**

**Solution (ii) :**

**Solution (iii) :**

12 players attempted 50 free throws each, and the number of free throws each player made was counted. There are 12 data values. Mean = 34.25 ; median = 34.5 ; range = 19 ; IQR = 6

**Example 2 :**

A birdwatcher counts and records the number of birds at a bird feeder every morning at 9:00 for several days.

12, 3, 8, 1, 1, 6, 10, 14, 3, 6, 2, 1, 3, 2, 7

(i) Make a frequency table.

(ii) Use histogram to represent the data.

(iii) Suppose the birdwatcher continues his observation for three more days and collects these new data values: 5, 18, and 2. How could we change the histogram to include the data ?

**Solution (i) :**

**Solution (ii) :**

Make a histogram.

The intervals are listed along the horizontal axis. The vertical axis shows the frequencies. For each interval, draw a bar to show the number of days in that interval. The bars should have equal widths. They should touch but not overlap.

**Solution (iii) :**

Sample answer : Add an interval from 17–20 to show a bar 1 unit high for the new data value of 18. Increase the bar heights for the intervals 1–4 and 5–8 by 1.

After having gone through the stuff given above, we hope that the students would have understood "How to group data in intervals".

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