Lara is a wildlife researcher. They were analyzing the mean and median lengths of 7 fish their team had observed. The fish all had different lengths between 15cm and 33cm. Lara found out that they were misreading the longest length. It was actually 88cm, not 33cm. How will this length increasing affect the mean and median? Choose 1 answer: (A) Both the mean and median will increase. B The mean will increase, and the median will stay the same. (C) The mean will increase, and the median will decrease. (D) The mean will stay the same, and the median will increase.

Question

Lara is a wildlife researcher. They were analyzing the mean and median lengths of 7 fish their team had observed. The fish all had different lengths between  15cm and  33cm. Lara found out that they were misreading the longest length. It was actually  88cm, not  33cm. How will this length increasing affect the mean and median? Choose 1 answer: (A) Both the mean and median will increase. B The mean will increase, and the median will stay the same. (C) The mean will increase, and the median will decrease. (D) The mean will stay the same, and the median will increase.

Bytelearn · Accepted Answer

Mean and Median Properties: Lara is analyzing the lengths of 7 fish. To understand how the change in the longest fish length affects the mean and median, we first need to consider the properties of mean and median. The mean is the average of all values, so if one value increases, the mean will also increase. The median is the middle value when all values are ordered from least to greatest. Since there are 7 fish, the median is the length of the 4th fish. Changing the length of the longest fish (the 7th fish) does not affect the position of the median unless the new length causes a shift in the order, which is not the case here.Calculating Original Mean: To calculate the original mean, we would add up all the fish lengths and divide by 7. However, we do not have the exact lengths of the first 6 fish, only that they are between 15cm and 33cm. Since the longest fish was originally thought to be 33cm, the mean was calculated with this value. With the new length of 88cm, we will add this to the sum of the other 6 fish lengths and then divide by 7 to find the new mean.Determining Original Median: The original median is the length of the 4th fish. Since we are told that all fish had different lengths and the longest was 33cm, the median would be less than or equal to 33cm. With the longest fish now being 88cm, the median remains the length of the 4th fish, which is unchanged because the order of the first 6 fish lengths is still the same.Effect of Longest Fish Length Change: Therefore, the mean will increase because the sum of the lengths is now greater with the 88cm fish included. The median will stay the same because it is determined by the middle value, which is unaffected by the change in the longest fish length.

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