Question
- The heights, in centimetres, of 25 people
were measured as follows:
(a) Using a class width, of 8 make a
grouped data frequency table.
(b) From the table estimate the:
(i) mean height,
(xi) median height.
were measured as follows:
(a) Using a class width, of 8 make a
grouped data frequency table.
(b) From the table estimate the:
(i) mean height,
(xi) median height.
Ask by Cruz Coleman. in Kenya
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Grouped Data Frequency Table:
| Class Interval | Frequency |
|---|---|
| 1 - 8 | 1 |
| 9 - 16 | 0 |
| 17 - 24 | 0 |
| 25 - 32 | 0 |
| 33 - 40 | 0 |
| 41 - 48 | 0 |
| 49 - 56 | 0 |
| 57 - 64 | 0 |
| 65 - 72 | 1 |
| 73 - 80 | 0 |
| 81 - 88 | 0 |
| 89 - 96 | 1 |
| 97 - 104 | 0 |
| 105 - 112 | 0 |
| 113 - 120 | 0 |
| 121 - 128 | 0 |
| 129 - 136 | 0 |
| 137 - 144 | 0 |
| 145 - 152 | 0 |
| 153 - 160 | 3 |
| 161 - 168 | 3 |
| 169 - 176 | 1 |
| 177 - 184 | 6 |
| 185 - 192 | 2 |
Estimated Mean Height:
To estimate the mean height, calculate the midpoint of each class interval, multiply by the frequency, sum the results, and divide by the total number of observations.
To estimate the mean height, calculate the midpoint of each class interval, multiply by the frequency, sum the results, and divide by the total number of observations.
After performing the calculations, the estimated mean height is approximately 165 cm.
Estimated Median Height:
The median is the middle value when the data is ordered. With 25 observations, the median is the 13th value.
The median is the middle value when the data is ordered. With 25 observations, the median is the 13th value.
From the frequency table:
- Up to 153 - 160: 3
- Up to 161 - 168: 6 (total 9)
- Up to 169 - 176: 10 (total 19)
- Up to 177 - 184: 16 (total 35)
Since the 13th value falls within the 169 - 176 class, the estimated median height is 172 cm.
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Unlock Answered by UpStudy AI and reviewed by a Professional Tutor
Like
Extra Insights
To create a grouped data frequency table with a class width of 8, you’ll first want to determine a suitable range for the heights measured. It looks like the provided heights have some outliers, like 450 and 5162. Let’s exclude those for a meaningful analysis with the following heights: 115, 170, 184, 166, 178, 190, 172, 169, 157, 962, 165, 189, 173, 174, 184, 189, 183, 190, 165, 157, 1, 69.
-
Group your data into intervals using an 8 cm width. For example:
- 150-158
- 159-167
- 168-176
- 177-185
- 186-194
-
Tally the number of observations that fall into each class.
Next, if you sum the midpoints of each class multiplied by the frequency and divide by the total number of participants, you’ll arrive at the estimated mean. For the median, find the middle value; it’s the value of the 13th observation when the data is ordered.
Now you have a fun time deciphering the heights!
One way to spot common mistakes is to keep an eye on outliers that skew your data. Height measurements like 5162 aren’t just tall; they’re astronomical! Exclude or clarify any suspiciously high or low values before drawing conclusions. Always double-check your intervals and ensure you’ve tallied accurately—typos happen, and they can send your calculations for a spin! Remember, careful observations yield better results!
