The answers to Erica’s question depends on other students’ score and Erica’s score in relation to them. These questions can be answered by organizing, analyzing, and interpreting the data set. This is where the Z-statistics and Z-Score come to play. She is curious what the average marks is for the class room. She is curious what percentage of the students have scored lower than her and what percentage of students have scored more than her. She is curious if majority of the students have scored higher or lower than her. Erica scores 62 marks out of 100 and is curious if she has scored better than the average. For example, let’s say the test scores of the students in a class are published. In simpler terms, the Z score is the value of the deviation of a single data from its group mean value represented in terms of standard deviationĪ set of data only makes sense if any relevant information could be extracted from it. It is represented in terms of standard deviation.
Z score of a value defines how far or close the position of a raw value is from the mean value of the set of data. It is a raw value’s relationship to a set of values. Z score is the position of a single data with respect to its mean value which is defined in terms of standard deviation. More technically it’s a measure of how many standard deviations below or above the population mean a raw score is. Or you can use the Online Percentage Calculator.Simply put, a z-score (also called as standard score) gives you an idea of how far from the mean a data point is. Multiply resultant value by 100 to get a percentage score.
3) Join the X and Y axisĪs a result, we get 0.71566 4) Convert resultant value into percentage The second step is to look at the second decimal number on X-axis. Now we have to find out the corresponding probability from the table. In John's case, we will use the positive table because we get a positive z-score of 0.57.
Similarly, if we get a negative z-score, then we will use the negative table.
If we get a z-score positive then we will use a positive table. So, keep it handy.Īs we all know that there are two z-tables with positive and negative values. For that, we will use a Z-Table (or Standard Normal Distribution Table). To check how well John performed, we need to find the percentage of highest and lowest scores of other students.
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