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 12 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 = 25 min throw = 8
range = max - min = 17
2 how many intervals? lets use 5 for this
3 interval width = range / 5 = 3.4 round up → 3.5
4 lows → 1st at minimum... each interval low = previous low + rounded width
5 highs → each interval high = previous high + rounded width
b
intervals
from low to high
frequencies
relative
frequencies
cumulative
frequencies
1 8 - 11.4
2 11.5 - 14.9
3 15 - 18.4
4 18.5 - 21.9
5 22 - 25.4
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: Count frequencies

Count how many data points fall into each interval.
For interval \(8 - 11.4\): The data points are \(8,11,11\). Frequency \(f_1 = 3\)
For interval \(11.5 - 14.9\): The data points are \(12,14,13,14\). Frequency \(f_2=4\)
For interval \(15 - 18.4\): The data points are \(15,15,17,15,18,18\). Frequency \(f_3 = 6\)
For interval \(18.5 - 21.9\): The data points are \(19,20,20,19,16\). Frequency \(f_4=5\)
For interval \(22 - 25.4\): The data points are \(23,23,24,25,23\). Frequency \(f_5 = 5\)

Step2: Calculate relative frequencies

The total number of data points \(n=3 + 4+6 + 5+5=23\)
Relative frequency \(rf_i=\frac{f_i}{n}\)
For \(i = 1\): \(rf_1=\frac{3}{23}\approx0.130\)
For \(i = 2\): \(rf_2=\frac{4}{23}\approx0.174\)
For \(i = 3\): \(rf_3=\frac{6}{23}\approx0.261\)
For \(i = 4\): \(rf_4=\frac{5}{23}\approx0.217\)
For \(i = 5\): \(rf_5=\frac{5}{23}\approx0.217\)

Step3: Calculate cumulative frequencies

Cumulative frequency \(cf_i=\sum_{j = 1}^{i}f_j\)
For \(i = 1\): \(cf_1 = 3\)
For \(i = 2\): \(cf_2=3 + 4=7\)
For \(i = 3\): \(cf_3=3+4 + 6=13\)
For \(i = 4\): \(cf_4=3+4 + 6+5=18\)
For \(i = 5\): \(cf_5=3+4 + 6+5+5=23\)

Answer:

INTERVALS from Low to High	Frequencies	Relative Frequencies	Cumulative Frequencies
\(11.5 - 14.9\)	\(4\)	\(0.174\)	\(7\)
\(15 - 18.4\)	\(6\)	\(0.261\)	\(13\)
\(18.5 - 21.9\)	\(5\)	\(0.217\)	\(18\)
\(22 - 25.4\)	\(5\)	\(0.217\)	\(23\)