Question

Response Questions Part A To C A. The hisbgram concems the number of seeds producad by a sample of 50 pants. Each bar includes the right boundary value 0 10 20 30 40 50 60 70 80 90 100 Number of seeds The median mumber ofseeds produced is more than 50 and less than orequal to 60 more than 20 and less than orequal to 30 more than 40 and less than orequal to 50 more than 30 and less than orequal to 40 B. A machine automatically weighs hebiomass of harvested plants. Itreports that the mean biomass of 50 plants is 125 g and the median biomass was 130 g A quality control inspection showed hat one plant was measured incorrectly because some soil had not been removed. The recordad weight was 200 g, but tha actual weight was 175 g Which statement is correct? The corectad median will not change, because the eroneous and corrected values are both larger than tha original median. Both the corected mean and median will decrease, because the corrected value is lower compared the original value. Both the corrected mean and median will not dan . because the erroneous and corrected values are both larger han the original mean and median Tha comec tad median wil dacraase. because the correctad valua is lowr compared to the original valve C. Consider choosing five numbers from 1 to 10, inclusive, with repetitions allowed. Which of the choices is correct? The set 1,2,9, 10 has the largest possible standard deviation. The set 7, 8,9, 10 has the largest possible mean. The set 3, 3, 3, 3 has the smallest possible standard deviation. The set 1, 1,9, 10 has the widest possible ?? QR

Answer 1

A. The distribution of the seeds and number of plants in given in the table.
The 25th plant(Middle value of the number of plants )lies in 20 to 30 seeds range.

Number of seeds Numbers of plants 0 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 100 12 13 5 Median (Middle value of number of plants) 4 50

Median number of seeds producted is more than 20 and less than or equal to 30

B.

Median value is the middle value obtained after arranging all the observation in ascending order, in this case the middle value is 130 g(median which is given before correction).
The correct weight and original weight of the biomass is above the median value, hence the median value remains unchange.

However the mean would change, as it the sum of the values. In this case mean gets reduced.

C.
The set 1,2,9,10 has the largest possible standard deviation

Standard deviation is 1,2,9,10 is 4.03.
but if the number were 1,1,10,10 then the std. deviation would be 4.5 which is the max.
Hence statement is incorrect

The set 7,8,9,10 has the larget possible mean.
Mean of 7,8,9,10 is 8.5 but if the numbers were 10,10,10,10 the mean is 10 which is the largest.
Hence statement is incorrect.

The set 3,3,3,3 has the smallest possible standard deviation
Here the standard deviation is zero which is the smallest std. dev.
Hence statement is correct.

The set 1,1,9,10 has the widest possible IQRHere the IQR is 8.5,
if the numbers were 1,1,10,10 IQR is -9 which is greater.
Hence statement is incorrect.