Math

Question Find the 43rd and 53rd percentiles of the ages of 29 Academy Award winning best actors, given in ascending order: 24,27,27,30,30,36,37,37,37,39,42,45,46,47,48,49,50,51,51,56,61,63,64,69,70,71,77,78,7824, 27, 27, 30, 30, 36, 37, 37, 37, 39, 42, 45, 46, 47, 48, 49, 50, 51, 51, 56, 61, 63, 64, 69, 70, 71, 77, 78, 78.

Studdy Solution

STEP 1

Assumptions
1. The ages listed are in ascending order.
2. There are 29 data points (ages of Academy Award winning best actors).
3. Percentiles are calculated using the formula Pk=k(n+1)100P_k = \frac{k(n+1)}{100}, where PkP_k is the kkth percentile and nn is the number of data points.
4. If the result of the formula is not an integer, we will interpolate between the two nearest data points.

STEP 2

First, we will calculate the position of the 4343rd percentile in the data set using the formula for percentiles.
P43=43(29+1)100P_{43} = \frac{43(29+1)}{100}

STEP 3

Now, plug in the values to calculate the position of the 4343rd percentile.
P43=43(30)100P_{43} = \frac{43(30)}{100}

STEP 4

Calculate the position of the 4343rd percentile.
P43=1290100=12.9P_{43} = \frac{1290}{100} = 12.9

STEP 5

Since the position 12.912.9 is not an integer, we will need to interpolate between the 1212th and 1313th data points to find P43P_{43}. The 1212th data point is the age 4242 and the 1313th data point is the age 4545.

STEP 6

Interpolate between the 1212th and 1313th data points.
P43=42+(4542)×0.9P_{43} = 42 + (45 - 42) \times 0.9

STEP 7

Calculate the 4343rd percentile.
P43=42+3×0.9=42+2.7=44.7P_{43} = 42 + 3 \times 0.9 = 42 + 2.7 = 44.7
The 4343rd percentile is approximately 44.744.7 years.

STEP 8

Next, we will calculate the position of the 5353rd percentile in the data set using the same formula for percentiles.
P53=53(29+1)100P_{53} = \frac{53(29+1)}{100}

STEP 9

Now, plug in the values to calculate the position of the 5353rd percentile.
P53=53(30)100P_{53} = \frac{53(30)}{100}

STEP 10

Calculate the position of the 5353rd percentile.
P53=1590100=15.9P_{53} = \frac{1590}{100} = 15.9

STEP 11

Since the position 15.915.9 is not an integer, we will need to interpolate between the 1515th and 1616th data points to find P53P_{53}. The 1515th data point is the age 4848 and the 1616th data point is the age 4949.

STEP 12

Interpolate between the 1515th and 1616th data points.
P53=48+(4948)×0.9P_{53} = 48 + (49 - 48) \times 0.9

STEP 13

Calculate the 5353rd percentile.
P53=48+1×0.9=48+0.9=48.9P_{53} = 48 + 1 \times 0.9 = 48 + 0.9 = 48.9
The 5353rd percentile is approximately 48.948.9 years.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord