Question
The histogram shows the ages of a group of youth and young adults attending a summer camp.
bottom row(age):8,9,10,11,12,13,14,15,16,17,18,19,20
side column(frequency):1,7,13,11,8,7,5,4,2,1,1,1,1
Interpret the histogram. Drag and drop the correct values to complete each sentence.
Note: Some drop values will not be used.
The shape of the data is (Response area) and skewed (Response area).
The mode age is (Response area). The approximate median age is (Response area).
The approximate mean age is (Response area).
An estimate for the standard deviation is (Response area).
Response area options:
uniform
unimodal
bimodal
left
right
2.5
5
10
11
12
bottom row(age):8,9,10,11,12,13,14,15,16,17,18,19,20
side column(frequency):1,7,13,11,8,7,5,4,2,1,1,1,1
Interpret the histogram. Drag and drop the correct values to complete each sentence.
Note: Some drop values will not be used.
The shape of the data is (Response area) and skewed (Response area).
The mode age is (Response area). The approximate median age is (Response area).
The approximate mean age is (Response area).
An estimate for the standard deviation is (Response area).
Response area options:
uniform
unimodal
bimodal
left
right
2.5
5
10
11
12
Answers
GPT-4o mini
To interpret the histogram, we will analyze the shape, mode, median, mean, and standard deviation based on the frequency of ages.
1. For the shape of the data and its skewness:
- The data shows a concentration of younger ages, with frequencies decreasing as age increases. This suggests that the data is left-skewed.
- **Shape of the data:** unimodal
- **Skewed:** left
2. To find the mode:
- The mode is the age with the highest frequency, which is 11 (frequency = 13).
- **Mode age:** 11
3. To approximate the median:
- To find the median, we look for the middle value in the cumulative frequency. The total frequency is 69 (1+7+13+11+8+7+5+4+2+1+1+1+1), and the median is the 35th value (69/2 = 34.5, the average of the 34th and 35th).
- Checking the cumulative frequency:
- Age 8: 1
- Age 9: 8 (1+7)
- Age 10: 21 (8+13)
- Age 11: 32 (21+11)
- Age 12: 40 (32+8)
- The 35th value falls within age 12.
- **Approximate median age:** 12
4. To estimate the mean:
- The mean can be calculated by weighting each age by its frequency, but without calculation, based on the distribution, we can estimate it to be around 10.
- **Approximate mean age:** 10
5. For an estimate of the standard deviation:
- Generally, for a rough estimate based on the spread of data:
- A reasonable estimate for the standard deviation, given the age range and how it spreads, would be around 2.5.
- **Estimate for the standard deviation:** 2.5
Combining these interpreted values, the final sentences will be:
- The shape of the data is **unimodal** and skewed **left**.
- The mode age is **11**.
- The approximate median age is **12**.
- The approximate mean age is **10**.
- An estimate for the standard deviation is **2.5**.
1. For the shape of the data and its skewness:
- The data shows a concentration of younger ages, with frequencies decreasing as age increases. This suggests that the data is left-skewed.
- **Shape of the data:** unimodal
- **Skewed:** left
2. To find the mode:
- The mode is the age with the highest frequency, which is 11 (frequency = 13).
- **Mode age:** 11
3. To approximate the median:
- To find the median, we look for the middle value in the cumulative frequency. The total frequency is 69 (1+7+13+11+8+7+5+4+2+1+1+1+1), and the median is the 35th value (69/2 = 34.5, the average of the 34th and 35th).
- Checking the cumulative frequency:
- Age 8: 1
- Age 9: 8 (1+7)
- Age 10: 21 (8+13)
- Age 11: 32 (21+11)
- Age 12: 40 (32+8)
- The 35th value falls within age 12.
- **Approximate median age:** 12
4. To estimate the mean:
- The mean can be calculated by weighting each age by its frequency, but without calculation, based on the distribution, we can estimate it to be around 10.
- **Approximate mean age:** 10
5. For an estimate of the standard deviation:
- Generally, for a rough estimate based on the spread of data:
- A reasonable estimate for the standard deviation, given the age range and how it spreads, would be around 2.5.
- **Estimate for the standard deviation:** 2.5
Combining these interpreted values, the final sentences will be:
- The shape of the data is **unimodal** and skewed **left**.
- The mode age is **11**.
- The approximate median age is **12**.
- The approximate mean age is **10**.
- An estimate for the standard deviation is **2.5**.