A histogram is a graph that groups numerical data into equal-width ranges (bins) and shows the frequency of values in each range using adjacent bars that touch. Unlike bar graphs, histograms display the distribution shape of continuous data.
Unlike bar graphs for categories (red, blue, green), histograms are for numbers grouped into ranges. Test scores 60-70, 70-80, 80-90... The bars touch because the data is continuous - there's no gap between 69.9 and 70.0.
Showing a random 20 of 50 problems.
Example 1
medium
A histogram has bins 0-10,10-20,20-30,30-40 with frequencies 6,8,4,2. Using bin midpoints, what is the estimated mean?Estimate the mean using bin midpoints.
Example 2
medium
A histogram has bins of width 5 and frequencies 2, 4, 6, 8 for bins starting at 0. Estimate the mean using bin midpoints.Estimate the mean using bin midpoints.
Example 3
medium
A histogram has bins of frequencies 4, 6, 10. What percent of the data is in the largest bin?
Example 4
hard
A histogram of incomes ($ thousands) has bins of width 20. The bin 40-60 has frequency 30 out of 100. What is the bin's frequency density (per $ thousand)?
Example 5
challenge
A histogram of 200 values has bins 0-25,25-50,50-75,75-100 with frequencies 40,60,70,30. Using interpolation, estimate the 80th percentile.Estimate the 80th percentile using interpolation.
Example 6
easy
A histogram has bins 0-10, 10-20, 20-30 with frequencies 4, 7, 2. How many data values are in the 10-20 bin?Read the frequency of the 10–20 bin.
Example 7
medium
A histogram of 30 test scores has bins 50-60 (6), 60-70 (10), 70-80 (9), 80-90 (5). What percent of students scored 70 or higher?What percent of students scored 70 or higher?
Example 8
easy
A histogram has bin width 10 starting at 0. Which bin does the value 47 fall in (left-inclusive convention)?
Example 9
medium
A histogram has bins of widths 10 with frequencies 4,8,10,6,2. What is the relative frequency of the third bin?What is the relative frequency of the third bin?
Example 10
medium
A histogram has bins of equal width 5 starting at 0, frequencies 1,3,5,4,2. Estimate the mean using midpoints.Estimate the mean using bin midpoints.
Example 11
easy
A histogram has bins 0-10, 10-20, 20-30, 30-40 with frequencies 3,5,8,4. How many data points in total?How many data points in total?
Example 12
medium
A histogram has bins 0-20,20-40,40-60,60-80 with frequencies 5,10,20,15. In which bin does the median lie (n=50)?In which bin does the median lie? (n = 50)
Example 13
easy
A histogram has bins 0-5 and 5-10 with frequencies 4 and 6. What fraction is in the lower bin?What fraction of the data is in the lower bin?
Example 14
medium
Explain two differences between a histogram and a bar graph.
Example 15
easy
A histogram has 4 bins of frequency 2,4,6,8. What is the mode bin (range)?
Example 16
hard
A histogram has unequal-width bins: 0-10 (w=10, freq 20), 10-30 (w=20, freq 30). Which bin has higher frequency density?
Example 17
challenge
A histogram with frequencies 6, 9, 5 over bins 0-10, 10-20, 20-30 is claimed to have a mean of 14 using midpoints. Verify or correct it.Verify the estimated mean using bin midpoints.
Example 18
medium
A histogram is bimodal with peaks at the 10-20 and 40-50 bins. What does this suggest about the data?
Example 19
easy
Why do histogram bars touch but bar-graph bars don't?
Example 20
hard
A histogram changes from bin width 10 to bin width 20. What visual effect does this have on the appearance?