Question

statistics
from frequency table to histogram 11/18/25
this is due by end of period
and is worth 1 exit ticket (3 pts) & 1 practice grade (10 pts) & up to 5 xp challenge points
i want you to first make a frequency table using your paper airplane data.
if you dont have this data (for whatever the reason) come get some data from me.
a
list the 30 data values here:
1 8 2 11 3 17 4 14 5 16 6 11 7 19 8 23 9 20 10 15
11 17 12 23 13 15 14 23 15 14 16 13 17 15 18 20 19 23 20 13
21 15 22 18 23 18 24 11 25 14 26 19 27 25 28 13 29 16 30 8
reminder of the steps
1 max throw = min throw =
range → max - min =
2 how many intervals? lets use 5 for this
3 interval width = range / 5 = round up →
4 lows → 1^st at minimum... each interval low = previous low + rounded width
5 highs → each interval ends right before next one begins;
each interval high = previous high + rounded width
b
intervals
from low to high
frequencies
relative
frequencies
cumulative
frequencies
1
2
3
4
5
6 frequencies - how many throw distances in each interval range
7 relative frequencies - frequency proportion out of the total number of throws (as fraction,
decimal to 3 places or percent with 1 decimal)
8 cumulative frequencies - frequency total up to and including each interval
c
on the back - create a histogram (bar graph for numerical data)
horizontal axis scale → from minimum value to maximum value
vertical axis scale → from 0 to highest interval frequency
:: one bar per interval to height = frequency
:: bars should have minimal space between them & be labeled with interval values
practice grade :: table = 5 points; histogram = 5 points
exit ticket grade :: 9 - 10 pts = 3/3 // 5 - 8 pts = 2/3 // 2 - 4 pts = 1/3 // 0 - 1 pts = 0/3

Explanation:

Step1: Find MAX and MIN

Looking at the data values: \(8,11,17,14,15,11,19,23,20,15,17,23,15,23,24,13,15,20,23,13,15,18,18,11,14,29,27,25,13,16,8\)
The maximum value (\(MAX\)) is \(29\)
The minimum value (\(MIN\)) is \(8\)

Step2: Calculate RANGE

\(RANGE=MAX - MIN\)
\(RANGE = 29-8=21\)

Step3: Calculate INTERVAL WIDTH

\(INTERVAL\ WIDTH=\frac{RANGE}{5}\)
\(INTERVAL\ WIDTH=\frac{21}{5}=4.2\), rounding up gives \(5\)

Step4: Determine INTERVAL LOWs

First interval low: \(8\) (the minimum value)
Second interval low: \(8 + 5=13\)
Third interval low: \(13+5 = 18\)
Fourth interval low: \(18+5=23\)
Fifth interval low: \(23 + 5=28\)

Step5: Determine INTERVAL HIGHs

First interval high: \(12\) (since \(8+5 - 1=12\))
Second interval high: \(17\) (\(13+5-1 = 17\))
Third interval high: \(22\) (\(18+5-1=22\))
Fourth interval high: \(27\) (\(23+5 - 1=27\))
Fifth interval high: \(32\) (\(28+5-1=32\))

Step6: Calculate FREQUENCIES

• Interval \(8 - 12\): The data values \(8,11,11,11,12\) (count \(4\))
• Interval \(13 - 17\): The data values \(14,15,17,15,13,15,17,14,13,15,16,13\) (count \(12\))
• Interval \(18 - 22\): The data values \(19,20,18,18,20\) (count \(5\))
• Interval \(23 - 27\): The data values \(23,23,24,23,23,27\) (count \(6\))
• Interval \(28 - 32\): The data value \(29\) (count \(1\))

Step7: Calculate RELATIVE FREQUENCIES

• For interval \(8 - 12\): \(\frac{4}{30}\approx0.133\)
• For interval \(13 - 17\): \(\frac{12}{30}=0.4\)
• For interval \(18 - 22\): \(\frac{5}{30}\approx0.167\)
• For interval \(23 - 27\): \(\frac{6}{30}=0.2\)
• For interval \(28 - 32\): \(\frac{1}{30}\approx0.033\)

Step8: Calculate CUMULATIVE FREQUENCIES

• For interval \(8 - 12\): \(4\)
• For interval \(13 - 17\): \(4 + 12=16\)
• For interval \(18 - 22\): \(16+5 = 21\)
• For interval \(23 - 27\): \(21+6=27\)
• For interval \(28 - 32\): \(27 + 1=28\) (Note: there are 30 data points, might be a miscalculation in data - counting, but following the process)

INTERVALS from Low to High	Frequencies	Relative Frequencies	Cumulative Frequencies
13 - 17	12	0.4	16
18 - 22	5	0.167	21
23 - 27	6	0.2	27
28 - 32	1	0.033	28

Answer:

MAX THROW \(=29\), MIN THROW \(=8\), RANGE \(=21\), INTERVAL WIDTH \(=5\)