The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31 hours and the median is 27.2 hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 7th percentile of the data is 16 hours. Approximately how many families are in the sample? Round your answer to the nearest integer.

Question

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31 hours and the median is 27.2 hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 7th percentile of the data is 16 hours.  Approximately how many families are in the sample? Round your answer to the nearest integer.

James Kilian · Accepted Answer

The number of people turned ON television for 16 hours is 24.&amp;nbsp;The 7th percentile of the data is,&amp;nbsp;7%(n)=24&amp;nbsp;7100n=24&amp;nbsp;n=100724&amp;nbsp;n=342.8&amp;nbsp;n≈343&amp;nbsp;The total number of families in the sample is 343.

star233 · Accepted Answer

Given information:- Mean of the data, denoted as x¯, is 31 hours.- Median of the data, denoted as M, is 27.2 hours.- Number of families that turned on the television for 16 hours or less, denoted as n16, is 24.- The 7th percentile of the data, denoted as P7, is 16 hours.First, we can calculate the number of families that turned on the television for more than 16 hours by subtracting n16 from the total number of families:n−n16=n−24Next, we can calculate the 7th percentile in terms of position. Since P7 is the value at the 7th percentile, it means that approximately 7% of the families have a value less than or equal to 16 hours. This can be expressed as:7100×n=0.07nNow, we can set up an equation using the median value. The median is the value that separates the lower 50% from the upper 50% of the data. Since the median is given as 27.2 hours, it means that approximately 50% of the families have a value less than or equal to 27.2 hours. This can be expressed as:50100×n=0.5nSince the given mean is 31 hours, it implies that the sum of all values in the sample divided by the number of families should equal 31:[∑i=1nxin=31]The sum of all values can be expressed as:∑i=1nxi=n×x¯Substituting the given values, we get:n×x¯=31nNow, we have four equations:1. n−n16=n−242. 0.07n=163. 0.5n=27.24. n×x¯=31nWe can solve these equations simultaneously to find the value of n.

karton · Accepted Answer

Answer:343Explanation:Let&#039;s denote the number of families in the sample as N.Given information:- Mean (μ) = 31 hours- Median = 27.2 hours- 7th percentile = 16 hours- Number of families with 16 hours or less = 24To find the approximate number of families in the sample, we can use the following steps:1. We know that the mean (μ) is the sum of all values divided by the total number of values. Mathematically, it can be represented as:μ=∑i=1NxiNwhere xi represents the hours of television turned on for each family.2. The median is the middle value of a sorted dataset. Since we are given the median as 27.2 hours, we can infer that it is the value at the (N + 1)/2 position in the sorted dataset.3. We are also given that the 7th percentile is 16 hours. This means that 7% of the values in the dataset are less than or equal to 16 hours.4. Finally, we know that there are 24 families with 16 hours or less.To solve for N, we can use the information about the 7th percentile:- The 7th percentile represents the (7/100) * N position in the sorted dataset. In other words, there are approximately (7/100) * N values less than or equal to 16 hours.- Since we have 24 families with 16 hours or less, we can equate this to (7/100) * N and solve for N.(7/100)·N=24Solving the equation, we find:N=247/100=240.07≈342.86Rounding to the nearest integer, we can say that there are approximately 343 families in the sample.

user_27qwe · Accepted Answer

Step 1: Finding the number of families below the 7th percentile.We know that the 7th percentile is 16 hours. This means that approximately 7% of the families in the sample have watched 16 hours or less. Therefore, the number of families below the 7th percentile is approximately 0.07n.Step 2: Finding the number of families above the 7th percentile.To find the number of families above the 7th percentile, we need to subtract the number of families below the 7th percentile from the total number of families. Therefore, the number of families above the 7th percentile is approximately n−0.07n=0.93n.Step 3: Finding the number of families between the median and the 7th percentile.We know that the median is 27.2 hours and the 7th percentile is 16 hours. Therefore, the number of families between the median and the 7th percentile is approximately 0.5n−0.07n=0.43n.Step 4: Finding the number of families above the median.To find the number of families above the median, we need to subtract the number of families between the median and the 7th percentile from the total number of families above the 7th percentile. Therefore, the number of families above the median is approximately 0.93n−0.43n=0.5n.Step 5: Finding the number of families below the median.To find the number of families below the median, we need to subtract the number of families above the median from the total number of families below the 7th percentile. Therefore, the number of families below the median is approximately 0.07n−0.5n=−0.43n.Since the number of families cannot be negative, we can conclude that the number of families below the median is 0.Step 6: Finding the number of families below the 7th percentile and the median.The number of families below the 7th percentile and the median is the sum of the number of families below the 7th percentile and the number of families below the median. Therefore, the number of families below the 7th percentile and the median is approximately 0+0.07n=0.07n.Step 7: Finding the number of families above the median.The number of families above the median is the sum of the number of families above the 7th percentile and the number of families between the median and the 7th percentile. Therefore, the number of families above the median is approximately 0.93n+0.43n=1.36n.Step 8: Finding the total number of families.The total number of families is the sum of the number of families below the 7th percentile and the median and the number of families above the median. Therefore, 0.07n+1.36n=1.43n represents the total numberof families.Since we know that there are 24 families below 16 hours, we can set up the equation:0.07n=24Solving for n, we get:n=240.07n≈342.86Rounding to the nearest integer, the estimated number of families in the sample is 343.Therefore, the estimated number of families in the sample is 343.

The number of hours per week that the television is turned on is deter

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