As noted by Hyndman and Fan (1996) there are multiple definition of quantiles and different implementations, so it is very likely that you found different estimates calculated from the same data (each of them equally "correct"). I'm afraid that to mention all the differences I'd need to literally reproduce the paper in here, so maybe you should rather read it yourself, as it is available online:

Hyndman, R.J., & Fan, Y. (1996). Sample Quantiles in Statistical Packages. American Statistician, 50(4): 361-365.

Notice that quantile function for R (in fact implemented by Hyndman) enables you to calculate all the nine types of quantiles (using type parameter), check ?quantile to read more. So even R gave you only one of the possible estimates.

As about the estimates, types 1, 2, 3, 5, 6, 8, and 9 return the values reproduced in your book, type 7 (default in quantile function for R) is what you obtained and type 4 disagrees with both estimates.

As noted by Hyndman and Fan (1996) there are multiple definition of quantiles and different implementations, so it is very likely that you found different estimates calculated from the same data (each of them equally "correct"). I'm afraid that to mention all the differences I'd need to literally reproduce the paper in here, so maybe you should rather read it yourself, as it is available online:

Hyndman, R.J., & Fan, Y. (1996). Sample Quantiles in Statistical Packages. American Statistician, 50(4): 361-365.

Notice that quantile function for R (in fact implemented by Hyndman) enables you to calculate all the nine types of quantiles (using type parameter), check ?quantile to read more. So even R gave you only one of the possible estimates.

As about the estimates, types 1, 2, 3, 5, 6, 8, and 9 return the values reproduced in your book, type 7 (default in quantile function for R) is what you obtained and type 4 disagrees with both estimates.

As noted by Hyndman and Fan (1996) there are multiple definition of quantiles and different implementations, so it is very likely that you found different estimates calculated from the same data (each of them equally "correct"). I'm afraid that to mention all the differences I'd need to literally reproduce the paper in here, so maybe you should rather read it yourself, as it is available online:

Hyndman, R.J., & Fan, Y. (1996). Sample Quantiles in Statistical Packages. American Statistician, 50(4): 361-365.

Notice that quantile function for R (in fact implemented by Hyndman) enables you to calculate all the nine types of quantiles (using type parameter), check ?quantile to read more. So even R gave you only one of the possible estimates.

As noted by Hyndman and Fan (1996) there are multiple definition of quantiles and different implementations, so it is very likely that you found different estimates calculated from the same data (each of them equally "correct"). I'm afraid that to mention all the differences I'd need to literally reproduce the paper in here, so maybe you should rather read it yourself, as it is available online:

Hyndman, R.J., & Fan, Y. (1996). Sample Quantiles in Statistical Packages. American Statistician, 50(4): 361-365.

Notice that quantile function for R (in fact implemented by Hyndman) enables you to calculate all the nine types of quantiles (using type parameter), check ?quantile to read more. So even R gave you only one of the possible estimates.

As about the estimates, types 1, 2, 3, 5, 6, 8, and 9 return the values reproduced in your book, type 7 (default in quantile function for R) is what you obtained and type 4 disagrees with both estimates.