Question

raven is organizing her clothes. she recorded the type of each clothing item in the frequency table.
raven’s clothes
type\tfrequency
pants\t6
jeans\t2
dress\t4
shorts\t3
t - shirt\t10
in which table do the percentages represent the relative frequency of these clothing types?
a
raven’s clothes
type\tpercentage of all clothes
pants\t18%
jeans\t6%
dress\t12%
shorts\t9%
t - shirt\t30%

Explanation:

Step1: Calculate total number of clothes

First, we sum up all the frequencies. The frequencies are 6 (Pants), 2 (Jeans), 4 (Dress), 3 (Shorts), and 10 (T - Shirt). So the total number of clothes \(N=6 + 2+4 + 3+10=25\).

Step2: Calculate relative frequency for each type

• For Pants: The relative frequency is \(\frac{6}{25}=0.24 = 24\%\) (Wait, the option A has 18% for Pants, maybe we made a mistake? Wait, no, let's recalculate. Wait, 6 + 2+4 + 3+10: 6+2=8, 8 + 4=12, 12+3 = 15, 15+10=25. Correct. Then:
• Pants: \(\frac{6}{25}=0.24 = 24\%\)
• Jeans: \(\frac{2}{25}=0.08=8\%\)
• Dress: \(\frac{4}{25}=0.16 = 16\%\)
• Shorts: \(\frac{3}{25}=0.12 = 12\%\)
• T - Shirt: \(\frac{10}{25}=0.4=40\%\)

Wait, the given option A has different percentages. Maybe there is a miscalculation? Wait, maybe the original problem's option A is mis - printed or we misread. Wait, let's check again. Wait, the user's option A: Pants 18%, Jeans 6%, Dress 12%, Shorts 9%, T - Shirt 30%. Let's sum these percentages: 18 + 6+12 + 9+30=75%, which is not 100%, so option A is wrong. But maybe the user's problem has other options (not shown here). But assuming that we need to find the correct relative frequencies:

The correct relative frequencies are:

• Pants: \(\frac{6}{25}\times100 = 24\%\)
• Jeans: \(\frac{2}{25}\times100=8\%\)
• Dress: \(\frac{4}{25}\times100 = 16\%\)
• Shorts: \(\frac{3}{25}\times100=12\%\)
• T - Shirt: \(\frac{10}{25}\times100 = 40\%\)

Since the option A provided has incorrect percentages (sum to 75% instead of 100%), but maybe there are other options. However, if we assume that the user made a typo and the option A is supposed to have correct percentages, but based on the given numbers, the correct relative frequencies are as calculated above.

Answer:

To find the table with correct relative frequencies, we calculate the relative frequency for each clothing type as \(\text{Relative Frequency}=\frac{\text{Frequency of Type}}{\text{Total Number of Clothes}}\times100\%\). The total number of clothes is \(6 + 2+4 + 3+10 = 25\).

• Pants: \(\frac{6}{25}\times100=24\%\)
• Jeans: \(\frac{2}{25}\times100 = 8\%\)
• Dress: \(\frac{4}{25}\times100=16\%\)
• Shorts: \(\frac{3}{25}\times100 = 12\%\)
• T - Shirt: \(\frac{10}{25}\times100=40\%\)

Since the provided option A has incorrect percentages (summing to 75% instead of 100%), there might be an error in the option presentation. If we assume that the intended correct table (not fully shown here) should have these percentages, the correct relative frequencies are as calculated. If we strictly consider option A, it is incorrect as its percentages do not sum to 100% and the individual percentages do not match the calculated relative frequencies.