how to do histogram and relative- frequency histogram using the #s 1,5,5,6,7,4,8,7,6,5,5,6,7,6,6,5,8,9,9, 10,7,8,11,2,4,6,5,12,13,6,3,7,8,8,9,9,10,9,8,9
with five classes
To create a histogram and a relative-frequency histogram with five classes using the given numbers, you can follow these steps:
Step 1: Sort the numbers in ascending order:
1, 2, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 12, 13
Step 2: Calculate the range:
Range = maximum value - minimum value = 13 - 1 = 12
Step 3: Calculate the interval size:
Interval Size = Range / Number of Classes = 12 / 5 = 2.4 (round it up to the nearest whole number) = 3
Step 4: Determine the class boundaries:
Start with the minimum value, which is 1, and add the interval size until you reach the maximum value, which is 13.
Class 1: 1 - 3
Class 2: 4 - 6
Class 3: 7 - 9
Class 4: 10 - 12
Class 5: 13
Step 5: Count the frequencies:
Count how many numbers fall into each class interval.
Class 1: 1, 2, 3 (Frequency = 3)
Class 2: 4, 4, 5, 5, 5, 5, 5, 6 (Frequency = 8)
Class 3: 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8 (Frequency = 13)
Class 4: 9, 9, 9, 9, 9 (Frequency = 5)
Class 5: 10, 11, 12, 13 (Frequency = 4)
Step 6: Create the histogram:
A histogram represents the frequencies of the classes using bars. Each bar's height represents the frequency of that class.
Class 1: XXX
Class 2: XXXXXXXX
Class 3: XXXXXXXXXXXXX
Class 4: XXXXX
Class 5: XXXX
Step 7: Create the relative-frequency histogram:
A relative-frequency histogram represents the proportion or percentage of the frequencies for each class.
To calculate the relative frequency, divide each frequency by the total number of values, which is 40.
Class 1: 3/40 = 0.075 (or 7.5%)
Class 2: 8/40 = 0.2 (or 20%)
Class 3: 13/40 = 0.325 (or 32.5%)
Class 4: 5/40 = 0.125 (or 12.5%)
Class 5: 4/40 = 0.1 (or 10%)
Relative-Frequency Histogram Representation:
Class 1: |||
Class 2: ||||||||
Class 3: ||||||||||||||
Class 4: ||||
Class 5: ||||
Range = 1-13 giving you 14 different score values
14/5 = 2 4/5, so 3 would seem to be best interval size.
For each score, put an X in the appropriate interval. The number of X's in each interval will determine the height of the bar for that interval for a histogram.
Divided each interval frequency by the N (total number of scores) to get the relative frequency and use those values to determine the height of the vertical bars.