Question

. If median of the given arranged data is 345, find x 334, 337, 338, 341, 344, x, 347, 350, 352, 355 In the given data if 350 is removed, what will be the new median? 6. For what value of a, is the mode of the following data 99? 91, 94, 99, 92, 98, 99, a, 96, 91, 99, 94, 92, 94 20. Observe the given arranged data and find the mode and mean, if median is 30. 21, 22, 25, 25, 2x+ 1, 30, 30, 35, 36, 40​

1. Based on the arranged data, x is equal to 346 and the new median is 344 when 350 is removed.
2. For a value of 99, the mode of the given data is equal to 99.The mean and mode of the given arranged data are 29.4 and 30 respectively.

### What is a median?

A median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there’s an outlier in the data set.
Based on the arranged data, we can observe that the total number of observations is equal to 10. Thus, the median would be calculated as follows:
Median = (5th number + 6th number)/2
345 = (344 + x)/2
690 = 344 + x
x = 690 – 344
x = 346.
When 350 is removed, the new median would be given by:
Median = [334, 337, 338, 341, 344, 346, 347, 352, 355]
Median = 344.

### What is mode?

A mode can be defined as a statistical term that is used to denote the value that appears most often or occurs repeatedly in a given data set.
For a value of 99, the mode of the given data is equal to 99.

### Part 3.

Based on the arranged data, we can observe that the total number of observations is equal to 10. Thus, the median would be calculated as follows:
Median = (5th number + 6th number)/2
30 = (2x + 1 + 30)/2
60 = 2x + 31
2x = 60 – 31
x = 29/2
x = 14.5.
Mathematically, the mean for this data can be calculated by using the following formula:
Mean = [F(x)]/n
Mean = [21 + 22 + 25 + 25 + 30 + 30 + 30 + 35 + 36 + 40]/10
Mean = 294/10
Mean = 29.4.
Mode = 30.
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