﻿ Histogram Worksheet | Problems & Solutions

# Histogram Worksheet

Histogram Worksheet
• Page 1
1.
Which of the histograms shows the data in the stem and leaf plot correctly?

 a. Figure 1 b. Figure 2

#### Solution:

From the stem and leaf plot, intervals can be divided as 0-9, 10-19, 20-29, 30-39 and 40-49.

The height of each bar in the histogram indicates the number of data values in a particular range.
[Number of data values in a range is nothing but the number of leaves for a particular stem.]

Observe the heights of the bars in each range to match with the number of leaves for the particular stem.

It can be observed that the heights of the bars in histogram in Figure 2 matches with the number of leaves for the corresponding stems in the stem-and-leaf plot given.

So, Figure 2 is the histogram, which shows the data in the stem-and-leaf plot correctly.

2.
The stem and leaf plot represents the sales of a particular type of bouquet during 10 days. Which of the histograms represents the data?
 Stem Leaf 2 6 7 8 3 0 1 3 7 4 4 5 5 2

 a. Figure 1 b. Figure 2

#### Solution:

From the stem and leaf plot, the data can be divided into four intervals as 20 - 29, 30 - 39, 40 - 49 and 50 - 59.

Take the intervals on the horizontal axis and the frequency, that is the number of leaves in the interval along the vertical axis.

The number of data values in each interval are 3, 4, 2 and 1.

The values match with the heights of the bars in the figure 2.

So, the histogram in figure 2 represents the data in the stem and leaf plot correctly.

3.
The table represents the temperature inside a Snow Park with respect to hours. Which of the histograms represents the data correctly?
 Hours Temperature in Celsius 0 - 6 0.8 7 - 12 1.4 13 - 18 2 19 - 24 1.5

 a. Graph 3 b. Graph 2 c. Graph 1 d. Graph 4

#### Solution:

The heights of the bars in the histograms indicate the rise of temperature in degree celsius with respect to hours.

Observe the heights of the bars in the histograms to match with the values given in the table.

It can be observed that the heights of the bars in histogram of Graph 1 exactly match with the data in the table.

So, the histogram in Graph 1 represents the data given in the table correctly.

4.
The graph shows the telelphone bills of customers of a city. How many customers had telephone bills greater than $40?  a. 32 b. 22 c. 36 d. 40 #### Answer: (d) Correct answer : (4) 5. The following data is about the ovens sold at an appliance store each day. Which of the following shows the intervals of equal size to group the data? 7 9 12 4 15 10 9 11 14 12 16 18 17 19 21 20 23 22 24 25  a. 5-10, 10-15, 15-20, 20-25 b. 7-25 c. 7-20, 20-25 d. 7-15, 20-25 #### Solution: The data range from 7 to 25. Choose equal-size intervals that begin with multiples of 5. So, the multiple of 5 that is close to 7 is 5. Therefore, 5-10, 10-15, 15-20, 20-25 show the intervals of equal size to group the data. Correct answer : (1) 6. The data shows the grades of students in a test. Which of the following graphs represents the data on a histogram? 50 51 52 53 54 71 73 72 74 66 67 66 68 61 62 63 64 69 68 67 66 56 58 59 57 59 56  a. Graph 3 b. Graph 1 c. Graph 4 d. Graph 2 #### Solution: A histogram is a special type of bar graph used to show the frequency of data. In a histogram, there are no spaces between bars. Graph 1 has no gaps between bars. Therefore, Graph 1 represents the data on a histogram. Correct answer : (2) 7. The battery life for different brands of television remotes is given on a histogram. How many batteries would last for 30-45 hours?  a. 18 b. 12 c. 20 d. 14 #### Solution: In the histogram, the height of each bar represents the number of batteries that can last for a particular range of hours. Therefore, the number of batteries that would last for 30-45 hours is 12. Correct answer : (2) 8. The ages of different people entering a local pub are given as follows. Which of the following intervals will yield you the higher degree of accuracy? 21 23 25 21 26 23 22 24 29 27 32 31 30 19 18 20 21 22 23 25  a. 21-30 b. 21-23, 23-25, 25-27, 27-29, 29-31, 31-33 c. 21-25, 25-30 d. 20-30 #### Solution: Broad intervals that is less number of class intervals will yield only rough estimates while small class intervals yield high degree of accuracy. Therefore, the intervals 21-23, 23-25, 25-27, 27-29, 29-31, 31-33 yield high degree of accuracy. Correct answer : (2) 9. The following data is about the grades of students in a test. Which of the following show the intervals of equal size to group the data? 58 73 80 79 51 66 67 59 60 73 76 76 78 78 60 57 78 62 65  a. 51-65, 75-80 b. 50-55, 55-60, 60-65, 65-70, 70-75, 75-80 c. 51-55, 60-65, 70-75 d. 51-80 #### Solution: The data range from 51 to 80. Choose equal-size intervals that begin with multiples of 5. So, the multiple of 5 that is close to 51 is 50. Therefore, 50-55, 55-60, 60-65, 65-70, 70-75, 75-80 show the intervals of equal size to group the data. Correct answer : (2) 10. The discounts offered by a super market are shown in the table. Which of the histograms is the correct representation of the data?  Amount (in$) Discount% 1000 - 1999 2 2000 - 2999 4 3000 - 3999 6 4000 - 4999 8 5000 - 5999 10

 a. Figure 1 b. Figure 2 c. Figure 3 d. Figure 4

#### Solution:

The heights of the bars in the histogram indicate the discount offered (in %) for the corresponding amount (in \$).

Match the heights of the bars in each graph with the values in the table.

It can be observed that the heights of the bars in figure 1 match with the values in the table.

So, figure1 is the correct representation of the data.