Question

1. use the following histograms to answer each question

histogram a

histogram b

data values

data values

a) which distribution had collected more data? show how you know.

b) which distribution has a larger range? show or explain how you know.

c) which distribution is more likely to have a shape described as \skewed right?\

Explanation:

Step1: Calculate total frequency for Histogram A

Sum up frequencies: $1 + 1+3 + 4+6+5+7+6 = 33$

Step2: Calculate total frequency for Histogram B

Sum up frequencies: $2+4 + 8+5+2+1+1+1 = 24$
Since $33>24$, Histogram A has more data.

Step3: Find range for Histogram A

Range = Max - Min. Max is 50, Min is 0, so range is $50 - 0=50$

Step4: Find range for Histogram B

Max is 50, Min is 0, so range is $50 - 0 = 50$. Both have the same range.

Step5: Identify skewed - right distribution

In Histogram B, the tail extends to the right (frequencies decrease gradually for larger data - values), so it is skewed right.

Answer:

a) Histogram A, because its total frequency (33) is greater than Histogram B's (24).
b) Both have the same range of 50 (as maximum value is 50 and minimum is 0 for both).
c) Histogram B, as its tail extends to the right.