Consider the pea data: # peas in pod 2,3,4,5,6 and frequency 7, 9, 5, 3, 1: a. find the mean, median, mode and midrange number of peas per pod.
b. is the mean higher or lower than the median? What kind of skew does this indicate?
I assume that you can find the mean, median, mode and midrange.
Since the mean is more effected by deviant scores, it would be higher, indicating a positive skew. (I get this just by looking at the frequencies.)
PsyDAG you are a smart a
a. To find the mean, median, mode, and midrange number of peas per pod, follow these steps:
1. Calculate the product of the number of peas per pod and their corresponding frequencies:
Number of peas per pod: 2, 3, 4, 5, 6
Frequencies: 7, 9, 5, 3, 1
(2 x 7) + (3 x 9) + (4 x 5) + (5 x 3) + (6 x 1) = 14 + 27 + 20 + 15 + 6 = 82
2. Sum up the frequencies:
7 + 9 + 5 + 3 + 1 = 25
3. Mean:
The mean is calculated by dividing the result obtained in step 1 by the result obtained in step 2:
Mean = Sum of (Number of peas per pod x Frequencies) / Sum of Frequencies
Mean = 82 / 25 = 3.28 (rounded to two decimal places)
4. Median:
The median is the middle value when the data is arranged in ascending order. First, organize the data in ascending order:
Number of peas per pod: 2, 3, 4, 5, 6
Frequencies: 7, 9, 5, 3, 1
Now, calculate the cumulative frequency:
Cumulative frequency: 7, 16, 21, 24, 25
The median falls into the frequency interval that has the cumulative frequency value greater than or equal to (25 / 2) = 12.5. In this case, it is the 3rd interval (4 peas per pod with a frequency of 5).
Median = Lower boundary of the interval + ((n / 2) - Cumulative frequency of the preceding interval) x Width of the interval
Median = 4 + ((12.5 - 7) / 5) x 1
= 4 + (5.5 / 5)
= 4 + 1.1
= 5.1
So, the median is 5.1.
5. Mode:
The mode is the value that appears most frequently in the data. In this case, the number of peas per pod with the highest frequency is 3. Therefore, the mode is 3.
6. Midrange:
The midrange is calculated by finding the average of the smallest and largest values in the data set. In this case, the smallest value is 2, and the largest value is 6.
Midrange = (Smallest value + Largest value) / 2
= (2 + 6) / 2
= 8 / 2
= 4
So, the midrange is 4.
b. To determine whether the mean is higher or lower than the median and the kind of skew it indicates, compare their values:
Mean: 3.28
Median: 5.1
Since the mean (3.28) is lower than the median (5.1), it indicates a left-skewed distribution.