z =0 and P(X< x) = 0.5 Explanation: z = (x-xbar)/sd, where xbar is the estimated mean or average of the sample, sd is the standard deviation, and x is the value of the particular outcome. We change x to z so that we can use the normal distribution or t-tables tables, which are based on a zero mean and 1 standard deviation. For example: What is the probability that the mean value of the distribution is 5 or less, given the sample average is 5 and the sd is 2? The z-score would be (5-5)/2 which is equal to 0. The probability, if we assume the normal or t-distribution, is 0.50. (see normal distribution tables) I hope this makes sense to you. The normal distribution is symmetrical. Per the example, a sample average of 5 tells you there is equal chance of the population mean being above and below 5.
No.
No. But there can be more than one data point which has the same value as the mean for the set of numbers. Or there can be none that take the mean value.
The minimum data value in a data set is simply the lowest value of the set (easily found by arranging the set from lowest-highest values in an excel sheet or by hand).
50
false
When the data set consistys of a single value.
You Get The Mean
The least value of the data set is called the minimum.
Every unique value has a unique distance from the mean, which leads to a unique z-score.
Yes.
176
No.
The median is the middle value (or mean of the two middle values if there are an even number of values) and so is unaffected by an increase in the highest data value. It is still 90. The mean was 95, so the total for the data set was 95x100 = 9500. If the highest data value is increased by 200, the data set total is also increased by 200, giving a new data set total of 9500 + 200 = 9700, so the new mean is 9700/100 = 97.
15
It is a measure of the spread of the data around its mean value.
It is one of the key measures of a data set: it shows the value around which the observations are spread out.
No. But there can be more than one data point which has the same value as the mean for the set of numbers. Or there can be none that take the mean value.