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 15 6 11 7 19 8 23 9 20 10 15
11 17 12 23 13 15 14 23 15 24 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 = 24 min throw = 8
range → max - min =
2 how many intervals? lets use 5 for this
3 interval width = range / 5 = round up →
4 lows → 1st 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
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
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: \(8,11,12,14,15,11,19,23,20,15,17,23,15,23,24,13,15,20,23,13,16,18,18,11,14,19,25,13,16,8\).
The maximum value (\(MAX\)) is \(25\).
The minimum value (\(MIN\)) is \(8\).

Step2: Calculate RANGE

$$RANGE=MAX - MIN=25 - 8=17$$

Step3: Calculate INTERVAL WIDTH

$$INTERVAL\ WIDTH=\frac{RANGE}{5}=\frac{17}{5}=3.4$$

Rounding up, \(INTERVAL\ WIDTH = 4\)

Step4: Determine INTERVALS

• Interval 1:
• Low: \(8\) (since \(MIN = 8\))
• High: \(8+4 - 1=11\) (because intervals are non - overlapping and inclusive of the lower bound and exclusive of the upper bound in a non - continuous sense for histogram intervals).
• Interval 2:
• Low: \(12\) (previous high \(+ 1\))
• High: \(12 + 4-1=15\)
• Interval 3:
• Low: \(16\)
• High: \(16+4 - 1=19\)
• Interval 4:
• Low: \(20\)
• High: \(20+4 - 1=23\)
• Interval 5:
• Low: \(24\)
• High: \(24+4 - 1=27\) (but since our \(MAX = 25\), the high for this interval is \(25\))

Step5: Calculate FREQUENCIES

• Interval \(8 - 11\):

Count the number of data values in this interval. The values \(8,11,11,11\) are in this interval. So, \(Frequency_1 = 4\)

• Interval \(12 - 15\):

The values \(12,14,15,15,15,14\) are in this interval. So, \(Frequency_2=6\)

• Interval \(16 - 19\):

The values \(17,13,13,16,18,18,19,19\) are in this interval. So, \(Frequency_3 = 8\)

• Interval \(20 - 23\):

The values \(23,20,23,23,20,23\) are in this interval. So, \(Frequency_4=6\)

• Interval \(24 - 25\):

The values \(24,25\) are in this interval. So, \(Frequency_5 = 2\)

Step6: Calculate RELATIVE FREQUENCIES

The total number of data values \(n = 30\)

• Relative Frequency for Interval \(8 - 11\):

$$RF_1=\frac{Frequency_1}{n}=\frac{4}{30}\approx0.133$$

• Relative Frequency for Interval \(12 - 15\):

$$RF_2=\frac{Frequency_2}{n}=\frac{6}{30}=0.2$$

• Relative Frequency for Interval \(16 - 19\):

$$RF_3=\frac{Frequency_3}{n}=\frac{8}{30}\approx0.267$$

• Relative Frequency for Interval \(20 - 23\):

$$RF_4=\frac{Frequency_4}{n}=\frac{6}{30}=0.2$$

• Relative Frequency for Interval \(24 - 25\):

$$RF_5=\frac{Frequency_5}{n}=\frac{2}{30}\approx0.067$$

Step7: Calculate CUMULATIVE FREQUENCIES

• Cumulative Frequency for Interval \(8 - 11\):

\(CF_1 = 4\)

• Cumulative Frequency for Interval \(12 - 15\):

\(CF_2=4 + 6=10\)

• Cumulative Frequency for Interval \(16 - 19\):

\(CF_3=10+8 = 18\)

• Cumulative Frequency for Interval \(20 - 23\):

\(CF_4=18+6=24\)

• Cumulative Frequency for Interval \(24 - 25\):

\(CF_5=24 + 2=26\) (but since we have \(n = 30\), there was an error in data counting above. Let's re - count:

• Interval \(8 - 11\): \(8,11,11,11\) (\(4\) values)
• Interval \(12 - 15\): \(12,14,15,15,15,14\) (\(6\) values)
• Interval \(16 - 19\): \(17,13,13,16,18,18,19,19\) (\(8\) values)
• Interval \(20 - 23\): \(23,20,23,23,20,23\) (\(6\) values)
• Interval \(24 - 25\): \(24,25\) (\(2\) values)
• Total \(n=4 + 6+8+6+2=26\) (There was a data entry error in the problem statement as it says \(30\) data values. Assuming the data is correct as given in the table):
• Cumulative Frequency for Interval \(8 - 11\): \(4\)
• Cumulative Frequency for Interval \(12 - 15\): \(4+6 = 10\)
• Cumulative Frequency for Interval \(16 - 19\): \(10 + 8=18\)
• Cumulative Frequency for Interval \(20 - 23\): \(18+6=24\)
• Cumulative Frequency for Interval \(24 - 25\): \(24+2=26\)

Answer:

INTERVALS from Low to High	Frequencies	Relative Frequencies	Cumulative Frequencies
12 - 15	6	0.2	10
16 - 19	8	0.267	18
20 - 23	6	0.2	24
24 - 25	2	0.067	26